Scatterometry system and method

A system for use in simulating scatterometry response of a patterned structure for scatterometry analysis for the patterned structure, the system comprising:

• a data input module for receiving input data comprising a scatterometry model data of a patterned structure comprising a selected number of virtual segment data pieces indicative of a respective number of segments of the patterned structure along Z-axis through the structure;
• and data indicative of one or more parameters of a measurement scheme used in scatterometry measurements on the patterned structures;
• a matrix data processing module configured for processing each of the segment data pieces and determining a matrix [Ωn] comprising Z-axis derivatives of electromagnetic fields' response of the segment to incident field based on Maxwell's equations' solution, and transforming said matrix [Ωn] into an exponential term [∧n] corresponding to electromagnetic field interaction between two different points spaced along the Z-axis, said transforming comprising embedding said matrix [Ωn] in a series expansion of said matrix exponential term [∧n];
• a matrix multiplication processing module adapted for multiplying the approximated response matrices {[∧n]} corresponding to all the segment data pieces and determining a general propagation matrix [∧],
• a scattering matrix generator configured for utilizing the general propagation matrix [∧] and determining a scattering matrix of the patterned structure, and
• a simulation system configured to apply said input data indicative of the one or more parameters of the measurement scheme to said scattering matrix, thereby obtaining one or more simulated scatterometry signatures indicative of simulated response signals from the patterned structure, wherein the simulated scatterometry signature is a function of at least one parameter of the measurement scheme and corresponds to one or more points in a certain parametric space of said scatterometry model;
• and to measure one or more parameters of actual patterned structures, utilizing any of the obtained simulated scatterometry signatures of simulated response signals, for patterned structure process control that includes fitting measured signals of the actual patterned structures with any of the simulated response signals.

A non-transitory program storage device readable by machine, tangibly embodying a program of instructions executable by the machine to perform a method for use in scatterometry analysis for a patterned structure, comprising:

• (a) providing a scatterometry model of a patterned structure comprising a selected number of virtual segment data pieces indicative of a respective number of segments of the patterned structure along Z-axis through the structure;
• and
• (b) processing each of the virtual segment data pieces, said processing comprising:
• i) determining a matrix [Ωn] comprising Z-axis derivatives of electromagnetic fields' response of the segment to incident field based on Maxwell's equations' solution;
• ii) transforming said matrix [Ωn] into an approximated response matrix [∧n] corresponding to the electromagnetic field interaction between two different points spaced along the Z-axis, said transforming comprising embedding said matrix [Ωn] in a series expansion of said matrix exponential term [∧n];
• (c) determining a general propagation matrix [∧] by carrying out multiplication of the approximated response matrices {[∧n]};
• (d) utilizing the general propagation matrix [∧] to determine a scattering matrix for the patterned structure;
• (e) applying data indicative of a measurement scheme to said scattering matrix, thereby obtaining simulated data comprising one or more simulated scatterometry signatures indicative of simulated response signals from the patterned structure, the simulated scatterometry signature being a function of at least one parameter of the measurement scheme and corresponding to one or more points in a certain parametric space of said scatterometry model;
• and
• (f) measuring one or more parameters of actual patterned structures, utilizing any of the obtained simulated scatterometry signatures of simulated response signals, for patterned structure process control that includes fitting measured signals of the actual patterned structures with any of the simulated response signals.