N K Technology Ltd

Shuqiang Chen

Guoguang Li

Abdul Rahim Forouhi

Phillip Walsh

Methods and apparatus for optical characterization based on symmetry-reduced 2-D RCWA calculations are provided. The invention is applicable to gratings having a grating reflection symmetry plane. A sample can be illuminated at normal incidence or at a non-zero angle of incidence such that the plane of incidence is parallel to or identical with the symmetry plane. The diffracted field components are either symmetric or anti-symmetric with respect to the grating symmetry plane. This symmetry is exploited to provide a symmetry-reduced 2-D RCWA having reduced matrix dimension (by about a factor of two) that is mathematically equivalent to a conventional 2-D RCWA. For normal incidence on a grating having two reflection symmetry planes, a symmetry-reduced 2-D RCWA having reduced matrix dimension (by about a factor of four) is provided. This normal incidence RCWA can be used to approximately characterize a sample illuminated at non-normal incidence. Approximation accuracy can be improved by modifying either the grating depth or the grating refractive index.

Efficient characterization of symmetrically illuminated symmetric 2-D gratings

Improved computation of Fourier coefficients for modeling of 2-D grating diffraction is provided. Let f(x,y) be defined in a region &#x3a9;. Typically, f(x,y) is piecewise constant (since it is a grating permittivity or inverse permittivity) and takes on various constant values in several domains in &#x3a9;. Let D be one of these domains, having a general shape. According to the invention, D is approximated as a set of trapezoids, and f(x,y) is taken to have a constant value within each of the trapezoids. Since the Fourier coefficient of a constant defined on a trapezoidal region can be analytically evaluated, an analytic approximation to the Fourier coefficient of f(x,y) on D is provided by summing the contributions from each trapezoid.

Efficient calculation of grating matrix elements for 2-D diffraction

A system and a method for optical characterization of a symmetric grating illuminated at off-normal incident angle are provided, where the plane of incidence is parallel to the grating lines. In this case corresponding positive and negative diffraction orders have the same intensity and phase. Several approaches for exploiting this symmetry are given. The first approach is a symmetric rigorous coupled wave analysis (SRCWA) adapted to the symmetric case, which accounts for N positive and N negative diffraction orders with M=N+1 space harmonics, without approximation. Various approximation methods are also given. Approximate versions of the RCWA (or SRCWA) can be developed by neglecting polarization coupling for small angles of incidence. A normal incident angle calculation can be used to approximate a situation with a small angle of incidence. Refinements to this approximation include revision of grating depth or refractive indices to improve accuracy. Methods other than the RCWA can also be symmetry simplified according to the invention.

System and method for efficient characterization of diffracting structures with incident plane parallel to grating lines

A system and method for optical offset measurement is provided. An offset between two grating layers in a compound grating is measured by illuminating the gratings with light having a plane of incidence that is neither parallel with nor perpendicular to the grating lines. This non-symmetrical optical illumination allows determination of the sign and magnitude of the offset. Two measurements are performed at azimuthal angles separated by 180&#xb0;, and a difference of these measurements is calculated. Measurement of this difference allows determination of the offset (e.g., with a calibration curve). Alternatively, two compound gratings having a predetermined non-zero offset difference can be employed. This arrangement permits determination of the offsets without the need for a calibration curve (or for additional compound gratings), based on a linear approximation.

System and method for measuring overlay alignment using diffraction gratings

An apparatus and method for determining a physical parameter of features on a substrate by illuminating the substrate with an incident light covering an incident wavelength range &#x394;&#x3bb;, e.g., from 190 nm to 1000 nm, where the substrate is at least semi-transparent. A response light received from the substrate and the feature is measured to obtain a response spectrum of the response light. Further, a complex-valued response due to the feature and the substrate is computed and both the response spectrum and the complex-valued response are used in determining the physical parameter. A direct approximate phase measurement is provided when the response light is transmitted light.

Phase shift measurement using transmittance spectra

Optical characterization of lateral features of a pattern is provided. A plane-wave optical response is calculated for each feature. At least one of these plane-wave responses is calculated from an effective optical property (e.g., a waveguide modal refractive index). Such effective optical properties depend on feature geometry and on intrinsic material optical properties. The plane-wave responses for each feature are combined to generate a modeled pattern response. By fitting the modeled pattern response to a corresponding measured pattern response, estimates for pattern feature parameters are obtained. The use of an effective optical property improves model accuracy, especially for features having a size on the order of a wavelength or less, without significantly increasing computation time.

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Sunnyvale, CA, United States of America

Shuqiang Chen