Measuring critical dimensions of a semiconductor structure
First Claim
1. A method of model-based optical metrology to measure a critical dimension of a grating layer, the method comprising:
- illuminating an area of a geometrical structure of dispersive materials with incident electromagnetic radiation from an illuminator of a scatterometer apparatus, wherein the incident electromagnetic radiation is polarized;
measuring spectral components of the incident electromagnetic radiation reflected from the area using a detector of the scatterometer apparatus; and
using a computer for the scatterometer apparatus to determine parameter values for the semiconductor structure that minimize an objective function J which depends on differences between the measured spectral components and computed spectral components based on a parameterized geometrical model of the geometrical structure,wherein steps for determining the parameter values that minimize the objective function include;
computing ∇
pJ where p is a parameterized vector of the parameter values, wherein the parameter values comprise ƒ and
h, where h is a height of the grating layer, and ƒ
is a critical dimension fraction comprising the critical dimension divided by a pitch of the grating layer.
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Abstract
One embodiment relates to a method of model-based optical metrology. An area of a geometrical structure of dispersive materials on a substrate is illuminated with polarized incident electromagnetic radiation using an illuminator of a scatterometer apparatus. Spectral components of the incident electromagnetic radiation reflected from the area are measured using a detector of the scatterometer apparatus. Using a computer for the scatterometer apparatus, parameter values are determined that minimize an objective function which represents a difference between the measured spectral components and computed spectral components based on a parameterized model of the geometrical structure. Steps for determining the parameter values that minimize the objective function include: computing a solution to state equations driven by a function representing the incident electromagnetic radiation, and computing a solution to an adjoint to the state equations. Other embodiments and features are also disclosed.
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Citations
35 Claims
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1. A method of model-based optical metrology to measure a critical dimension of a grating layer, the method comprising:
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illuminating an area of a geometrical structure of dispersive materials with incident electromagnetic radiation from an illuminator of a scatterometer apparatus, wherein the incident electromagnetic radiation is polarized; measuring spectral components of the incident electromagnetic radiation reflected from the area using a detector of the scatterometer apparatus; and using a computer for the scatterometer apparatus to determine parameter values for the semiconductor structure that minimize an objective function J which depends on differences between the measured spectral components and computed spectral components based on a parameterized geometrical model of the geometrical structure, wherein steps for determining the parameter values that minimize the objective function include; computing ∇
pJ where p is a parameterized vector of the parameter values, wherein the parameter values comprise ƒ and
h, where h is a height of the grating layer, and ƒ
is a critical dimension fraction comprising the critical dimension divided by a pitch of the grating layer. - View Dependent Claims (2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16)
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17. An apparatus for optical metrology for measuring a critical dimension of a grating layer, the apparatus comprising:
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a polarized illuminator configured to illuminate an area of a geometrical structure of dispersive materials with incident polarized electromagnetic radiation; a detector for measuring spectral components of the incident electromagnetic radiation reflected from the area; and a data processing system comprising computer-readable code configured to determine parameter values that minimize an objective function J which depends on differences between the measured spectral components and computed spectral components based on a parameterized model of the geometrical structure, wherein the objective function J comprises - View Dependent Claims (18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28)
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29. A method for estimating a critical dimension of a grating layer from spectroscopic measurements, the method comprising:
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using an illuminator of a scatterometer apparatus to illuminate an area of a geometrical structure of dispersive materials with incident electromagnetic radiation; measuring spectral components of the incident electromagnetic radiation reflected from the area using a detector of the scatterometer apparatus; using a computer for the scatterometer apparatus to compute a solution to state equations driven by a function representing the incident electromagnetic radiation, wherein the state equations are derived from Maxwell'"'"'s equations with dispersive materials; using the computer for the scatterometer apparatus to compute a solution to an adjoint to the state equations, wherein the adjoint to the state equations has a source function which is a derivative of a measurement function as a function of the solution of the state equations; and using the computer for the scatterometer apparatus to determine parameter values for the semiconductor structure that minimize an objective function J which depends on differences between the measured spectral components and computed spectral components based on a parameterized geometrical model of the geometrical structure, wherein steps for determining the parameter values that minimize the objective function include; computing ∇
pJ where p is a parameterized vector of the parameter values, wherein the parameter values comprise ƒ and
h, where h is a height of the grating layer, and ƒ
is a critical dimension fraction comprising the critical dimension divided by a pitch of the grating layer. - View Dependent Claims (30, 31, 32, 33, 34, 35)
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Specification