Regression calibrated spectroscopic rotating compensator ellipsometer system with photo array detector

A method of calibrating a spectroscopic rotating compensator material system investigation system comprising the steps of:

• a. providing a spectroscopic rotating compensator material system investigation system comprising a source of a polychromatic beam of electromagnetic radiation, a polarizer, a stage for supporting a material system, an analyzer, a dispersive optics and at least one detector system which contains a multiplicity of detector elements, said spectroscopic rotating compensator material system investigation system further comprising at least one compensator(s) positioned at a location selected from the group consisting of:
• before said stage for supporting a material system;
• after said stage for supporting a material system;
• and
• both before and after said stage for supporting a material system;
• such that when said spectroscopic rotating compensator material system investigation system is used to investigate a material system present on said stage for supporting a material system, said analyzer and polarizer are maintained essentially fixed in position and at least one of said at least one compensator(s) is/are caused to continuously rotate while a polychromatic beam of electromagnetic radiation produced by said source of a polychromatic beam of electromagnetic radiation is caused to pass through said polarizer and said compensator(s), said polychromatic beam of electromagnetic radiation being also caused to interact with said material system, pass through said analyzer and interact with said dispersive optics such that a multiplicity of essentially single wavelengths are caused to simultaneously enter a corresponding multiplicity of detector elements in said at least one detector system;
• b. developing a mathematical model of said spectroscopic rotating compensator material system investigation system which comprises as calibration parameter variables polarizer azimuthal angle orientation, present material system PSI, present material system DELTA, compensator azimuthal angle orientation(s), matrix components of said compensator(s), and analyzer azimuthal angle orientation, which mathematical model is effectively a transfer function which enables calculation of electromagnetic beam intensity as a function of wavelength detected by a detector element, given intensity as a function of wavelength provided by said source of a polychromatic beam of electromagnetic radiation;
• c. causing a polychromatic beam of electromagnetic radiation produced by said source of a polychromatic beam of electromagnetic radiation, to pass through said polarizer, interact with a material system caused to be in the path thereof, pass through said analyzer, and interact with said dispersive optics such that a multiplicity of essentially single wavelengths are caused to simultaneously enter a corresponding multiplicity of detector elements in said at least one detector system, with said polychromatic beam of electromagnetic radiation also being caused to pass through said compensator(s) positioned at a location selected from the group consisting of:
• before said stage for supporting a material system;
• after said stage for supporting a material system;
• and
• both before and after said stage for supporting a material system;
• d. obtaining an at least two dimensional data set of intensity values vs. wavelength and a parameter selected from the group consisting of:
• angle-of-incidence of said polychromatic beam of electromagnetic radiation with respect to a present material system;
• and
• azimuthal angle rotation of one element selected from the group consisting of:
• said polarizer;
• and
• said analyzer;
• over time, while at least one of said at least one compensator(s) is caused to continuously rotate;
• e. performing a mathematical regression of said mathematical model onto said at least two dimensional data set, thereby evaluating calibration parameters in said mathematical model;
• said regression based calibration procedure evaluated calibration parameters serving to compensate said mathematical model for non-achromatic characteristics and non-idealities of said compensator(s), and for azimuthal angles of said polarizer, analyzer compensator(s).

A method of calibrating a spectroscopic rotating compensator material system investigation system comprising the steps of:

• a. providing a spectroscopic rotating compensator material system investigation system comprising a source of a polychromatic beam of electromagnetic radiation, a polarizer, a stage for supporting a material system, an analyzer, a dispersive optics and at least one detector system which contains a multiplicity of detector elements, said spectroscopic rotating compensator material system investigation system further comprising at least one compensator(s) positioned at a location selected from the group consisting of:
• before said stage for supporting a material system;
• after said stage for supporting a material system;
• and
• both before, and after said stage for supporting a material system;
• such that when said spectroscopic rotating compensator material system investigation system is used to investigate a material system present on said stage for supporting a material system, said analyzer and polarizer are maintained essentially fixed in position and at least one of said at least one compensator(s) is/are caused to continuously rotate while a polychromatic beam of electromagnetic radiation produced by said source of a polychromatic beam of electromagnetic radiation is caused to pass through said polarizer and said compensator(s), said polychromatic beam of electromagnetic radiation being also caused to interact with said material system, pass through said analyzer and interact with said dispersive optics such that a multiplicity of essentially single wavelengths are caused to simultaneously enter a corresponding multiplicity of detector elements in said at least one detector system;
• b. developing a mathematical model of said spectroscopic rotating compensator material system investigation system which comprises as calibration parameter variables polarizer azimuthal angle orientation, present material system PSI, present material system DELTA, compensator azimuthal angle orientation(s), matrix components of said compensator(s), and analyzer azimuthal angle orientation, which mathematical model is effectively a transfer function which enables calculation of electromagnetic beam intensity as a function of wavelength detected by a detector element, given intensity as a function of wavelength provided by said source of a polychromatic beam of electromagnetic radiation, said mathematical model providing equations for coefficients of terms in said transfer function, said coefficients of terms each being a function of identified calibration parameters;
• c. causing a polychromatic beam of electromagnetic radiation produced by said source of a polychromatic beam of electromagnetic radiation, to pass through said polarizer, interact with a material system caused to be in the path thereof, pass through said analyzer, and interact with said dispersive optics such that a multiplicity of essentially single wavelengths are caused to simultaneously enter a corresponding multiplicity of detector elements in said at least one detector system, with said polychromatic beam of electromagnetic radiation also being caused to pass through said compensator(s) positioned at a location selected from the group consisting of:
• before said stage for supporting a material system;
• after said stage for supporting a material system;
• and
• both before and after said stage for supporting a material system;
• d. obtaining an at least two dimensional data set of intensity values vs. wavelength and a parameter selected from the group consisting of:
• angle-of-incidence of said polychromatic beam of electromagnetic radiation with respect to a present material system;
• and
• azimuthal angle rotation of one element selected from the group consisting of:
• said polarizer;
• and
• said analyzer;
• over time, while at least one of said at least one compensator(s) is caused to continuously rotate and from said data set calculating numerical values for coefficients of terms in the transfer function for said spectroscopic rotating compensator material system investigation system;
• e. performing a mathematical regression of said mathematical model equations for coefficients of terms in said transfer function, onto said transfer function term coefficient values, thereby evaluating said calibration parameters;
• said regression based calibration procedure evaluated calibration parameters serving to compensate said mathematical model for non-achromatic characteristics and non-idealities of said compensator(s), and for azimuthal angles of said polarizer, analyzer compensator(s).

A spectroscopic rotating compensator material system investigation system comprising a source of a polychromatic beam of electromagnetic radiation, a polarizer, a stage for supporting a material system, an analyzer, a dispersive optics and at least one detector system which contains a multiplicity of detector elements, said spectroscopic rotating compensator material system investigation system further comprising at least one compensator positioned at a location selected from the group consisting of:

• before said stage for supporting a material system;
• after said stage for supporting a material system;
• and
• before and after said stage for supporting a material system;
• such that when said spectroscopic rotating compensator material system investigation system is used to investigate a material system present on said stage for supporting a material system, said analyzer and polarizer are maintained essentially fixed in position and at least one of said said at least one compensator(s) is caused to continuously rotate while a polychromatic beam of electromagnetic radiation produced by said source of a polychromatic beam of electromagnetic radiation is caused to pass through said polarizer and said compensator(s), said polychromatic beam of electromagnetic radiation being also caused to interact with said material system;
• said polychromatic beam of electromagnetic radiation being also, without further focusing, caused to pass through said analyzer and interact with said dispersive optics, said dispersive optics serving to form a plurality of essentially spacially offset orders when said polychromatic beam of electromagnetic radiation is caused to impinge thereupon, each said produced order comprising an essentially continuous spectrum of spacially separated electromagnetic beams of essentially single wavelengths, many of said essentially single wavelengths being present in two or more produced orders;
• such that in use first and second multiplicities of essentially single wavelength beams of electromagnetic radiation from first and second produced orders are simultaneously intercepted by, respectively, first and second detector systems, thereby enabling the simultaneous accessing of a first multiplicity of essentially single wavelengths by said first detector system and a second multiplicity of essentially single wavelengths by said second detector system, each of which first and second multiplicities of essentially single wavelengths intercepted by said first and second detector systems, respectively, includes specific first and second essentially single wavelength beams of electromagnetic radiation, said specific first and second essentially single wavelength beams of electromagnetic radiation being simultaneously intercepted by specific detector elements in said first and second detector systems respectively, even where electromagnetic beams of said specific first and second essentially single wavelengths are spacially situated to close to one another in a single produced order for separate photo detector array detector elements in a single detector system which intercepts said single order, to, simultaneously, access beams of electromagnetic radiation of both said specific first and second essentially single wavelengths, separately.