US 6,608,690 B2 · Optical profilometry of additional-material deviations in a periodic grating

Abstract

Disclosed is a method and system for measurement of periodic gratings which have deviations which result in more than two materials occurring along at least one line in the periodic direction. A periodic grating is divided into a plurality of hypothetical layers, each hypothetical layer having a normal vector orthogonal to the direction of periodicity, each hypothetical layer having a single material within any line parallel to the normal vector, and at least one of the hypothetical layers having at least three materials along a line in the direction of periodicity. A harmonic expansion of the permittivity ε or inverse permittivity 1/ε is performed along the direction of periodicity for each of the layers including the layer which includes the first, second and third materials. Fourier space electromagnetic equations are then set up in each of the layers using the harmonic expansion of the permittivity ε or inverse permittivity 1/ε, and Fourier components of electric and magnetic fields in each layer. The Fourier space electromagnetic equations are then coupled based on boundary conditions between the layers, and solved to provide the calculated diffraction spectrum.

Claims60

Dependent claims

A method for metrology of additional-material structural deviations of a nominal periodic structure by comparison of a measured diffraction spectrum from a target periodic structure with a calculated diffraction spectrum from a hypothetical deviated periodic structure defined by applying said additional-material structural deviations to said nominal periodic structure, said hypothetical deviated periodic structure having a direction of periodicity x, a direction of essentially-infinite extension y orthogonal to said direction of periodicity x, and a normal direction z orthogonal to said direction of periodicity x and said direction of extension y, calculation of said calculated diffraction spectrum comprising the steps of:

defining a plurality of layers parallel to the x-y plane and discretizing an x-z plane cross-section of said periodic structure into a plurality of stacked rectangular sections such that only two materials from said nominal periodic structure are within each of said plurality of layers, and only a single material lies along each line along the normal direction z in each of said plurality of layers in said hypothetical deviated periodic structure, and at least three materials are within at least one of said plurality of layers in said hypothetical deviated periodic structure;
performing a harmonic expansion of a function of the permittivity ε along said direction of periodicity x for each of said layers including said at least one of said plurality of layers in said hypothetical deviated periodic structure having said at least three materials therein;
setting up Fourier space electromagnetic equations in said each of said layers using said harmonic expansion of said function of the permittivity ε for said each of said layers and Fourier components of electric and magnetic fields;
coupling said Fourier space electromagnetic equations based on boundary conditions between said layers;
and
solving said coupling of said Fourier space electromagnetic equations to provide said calculated diffraction spectrum.

3 more elements

A method of generating the diffracted reflectivity associated with diffraction of electromagnetic radiation off a target periodic grating to determine structural properties of the target periodic grating, including:

dividing the target periodic grating into a plurality of hypothetical layers, at least one of the hypothetical layers formed across each of at least a first, second and third material, each of the at least first, second and third materials occurring along a direction of periodicity of the target periodic grating, each separate hypothetical layer having one of a plurality of possible combinations of hypothetical values of properties for that hypothetical layer;
generating sets of hypothetical layer data, each set of hypothetical layer data corresponding to a separate one of the plurality of hypothetical layers;
and
processing the generated sets of hypothetical layer data to generate the diffracted reflectivity that would occur by reflecting electromagnetic radiation off the periodic grating.

1 more element

dividing the target periodic grating into a plurality of hypothetical layers, at least one of the hypothetical layers formed across each of at least a first, second and third material occurring along a line parallel to a direction of periodicity of the target periodic grating;
performing an harmonic expansion of a function of the permittivity ε along the direction of periodicity of the target period grating for each of the hypothetical layers including the at least one of the plurality of layers formed across each of at least a first, second and third material;
setting up Fourier space electromagnetic equations in each of the hypothetical layers using the harmonic expansion of the function of the permittivity ε for said each of the hypothetical layers and Fourier components of electric and magnetic fields;
coupling the Fourier space electromagnetic equations based on boundary conditions between the layers;
and
solving the coupling of the Fourier space electromagnetic equations to provide a diffracted reflectivity.

3 more elements

A method of generating an expression of the permittivity of a target periodic grating having more than two materials in a periodic direction for use in an optical profilometry formalism for determining a diffracted reflectivity of the target periodic grating comprising:

dividing the target periodic grating into a plurality of hypothetical layers, at least one of the hypothetical layers formed across each of at least a first, second and third material occurring along a line parallel to a direction of periodicity of the target periodic grating;
subdividing at least one of the plurality of hypothetical layers into a plurality of hypothetical slabs to generate a plurality of hypothetical boundaries, each of the plurality of hypothetical boundaries corresponding to an intersection of at least one of the plurality of hypothetical layers with one of at least the first, second and third materials;
determining a permittivity function for each of the plurality of hypothetical layers;
completing a one-dimensional Fourier expansion of the permittivity function of each hypothetical layer along the direction of periodicity of the target periodic grating by summing the Fourier components over the plurality of hypothetical boundaries to provide harmonic components of the at least one permittivity function;
and
defining a permittivity harmonics matrix including the harmonic components of the Fourier expansion of the permittivity function.

3 more elements

A computer readable storage medium containing computer executable code for generating the theoretical diffracted reflectivity associated with diffraction of electromagnetic radiation off a target periodic grating to determine structural properties of the target periodic grating by instructing a computer to operate as follows:

divide the target periodic grating into a plurality of hypothetical layers, at least one of the hypothetical layers formed across each of at least a first, second and third material, each of the at least first, second and third materials occurring along a direction of periodicity of the target periodic grating, each separate hypothetical layer having one of a plurality of possible combinations of hypothetical values of properties for that hypothetical layer;
generate sets of hypothetical layer data, each set of hypothetical layer data corresponding to a separate one of the plurality of hypothetical layers;
and
process the generated sets of hypothetical layer data to generate the diffracted reflectivity that would occur by reflecting electromagnetic radiation off the periodic grating.

1 more element

A computer readable storage medium containing computer executable code for generating the diffracted reflectivity associated with diffraction of electromagnetic radiation off a target periodic grating to determine structural properties of the target periodic grating by instructing a computer to operate as follows:

divide the target periodic grating into a plurality of hypothetical layers, at least one of the hypothetical layers formed across each of at least a first, second and third material occurring along a line parallel to a direction of periodicity of the target periodic grating;
perform an harmonic expansion of a function of the permittivity εl(x) along the direction of periodicity of the target period grating for each of the hypothetical layers including the at least one of the plurality of layers formed across each of at least a first, second and third material;
set up Fourier space electromagnetic equations in each of the hypothetical layers using the harmonic expansion of the function of the permittivity εl(x) for said each of the hypothetical layers and Fourier components of electric and magnetic fields;
couple the Fourier space electromagnetic equations based on boundary conditions between the layers;
and
solve the coupling of the Fourier space electromagnetic equations to provide a diffracted reflectivity.

3 more elements

A computer readable storage medium containing computer executable code for generating an expression of the permittivity of a target periodic grating having more than two materials in a periodic direction for use in an optical profilometry formalism for determining a diffracted reflectivity of the target periodic grating by instructing a computer to operate as follows:

divide the target periodic grating into a plurality of hypothetical layers, at least one of the hypothetical layers formed across each of at least a first, second and third material occurring along a line parallel to a direction of periodicity of the target periodic grating;
subdivide at least one of the plurality of hypothetical layers into a plurality of hypothetical slabs to generate a plurality of hypothetical boundaries, each of the plurality of hypothetical boundaries corresponding to an intersection of at least one of the plurality of hypothetical layers with one of at least the first, second and third materials;
determine a permittivity function for each of the plurality of hypothetical layers;
complete a one-dimensional Fourier expansion of the permittivity function of each hypothetical layer along the direction of periodicity of the target periodic grating by summing the Fourier components over the plurality of hypothetical boundaries to provide harmonic components of the at least one permittivity function;
and
define a permittivity harmonics matrix including the harmonic components of the Fourier expansion of the permittivity function.

3 more elements

A system for generating a theoretical diffracted reflectivity associated with diffraction of electromagnetic radiation off a target periodic grating to determine structural properties of the target periodic grating, including a computer processor configured to:

divide the target periodic grating into a plurality of hypothetical layers, at least one of the hypothetical layers formed across each of at least a first, second and third material, each of the at least first, second and third materials occurring along a direction of periodicity of the target periodic grating, each separate hypothetical layer having one of a plurality of possible combinations of hypothetical values of properties for that hypothetical layer;
generate sets of hypothetical layer data, each set of hypothetical layer data corresponding to a separate one of the plurality of hypothetical layers;
and
process the generated sets of hypothetical layer data to generate the diffracted reflectivity that would occur by reflecting electromagnetic radiation off the periodic grating.

1 more element

A system of generating the diffracted reflectivity associated with diffraction of electromagnetic radiation off a target periodic grating to determine structural properties of the target periodic grating, including a computer microprocessor configured to:

divide the target periodic grating into a plurality of hypothetical layers, at least one of the hypothetical layers formed across each of at least a first, second and third material occurring along a line parallel to a direction of periodicity of the target periodic grating;
perform an harmonic expansion of a function of the permittivity ε along the direction of periodicity of the target period grating for each of the hypothetical layers including the at least one of the plurality of layers formed across each of at least a first, second and third material;
set up Fourier space electromagnetic equations in each of the hypothetical layers using the harmonic expansion of the function of the permittivity ε for said each of the hypothetical layers and Fourier components of electric and magnetic fields;
couple the Fourier space electromagnetic equations based on boundary conditions between the layers;
and
solve the coupling of the Fourier space electromagnetic equations to provide a diffracted reflectivity.

3 more elements

A system of generating an expression of the permittivity of a target periodic grating having more than two materials in a periodic direction for use in an optical profilometry formalism for determining a diffracted reflectivity of the target periodic grating including a computer processor configured to:

divide the target periodic grating into a plurality of hypothetical layers, at least one of the hypothetical layers formed across each of at least a first, second and third material occurring along a line parallel to a direction of periodicity of the target periodic grating;
subdivide at least one of the plurality of hypothetical layers into a plurality of hypothetical slabs to generate a plurality of hypothetical boundaries, each of the plurality of hypothetical boundaries corresponding to an intersection of at least one of the plurality of hypothetical layers with one of at least the first, second and third materials;
determine a permittivity function for each of the plurality of hypothetical layers;
complete a one-dimensional Fourier expansion of the permittivity function of each hypothetical layer along the direction of periodicity of the target periodic grating by summing the Fourier components over the plurality of hypothetical boundaries to provide harmonic components of the at least one permittivity function;
and
define a permittivity harmonics matrix including the harmonic components of the Fourier expansion of the permittivity function.

3 more elements

Dependencies are inferred from the claim text.

Optical profilometry of additional-material deviations in a periodic grating

Life of this patent

Optical profilometry of additional-material deviations in a periodic grating

Life of this patent

Abstract

Claims60