The characterization of nanostructured surfaces by scatterometry is an established method in wafer metrology.
From measured light diffraction patterns, critical dimensions (CD) of surface profiles are determined, i.e., line
widths, heights and other profile properties in the sub-micrometer range. As structures become smaller and
smaller, shorter wavelengths like extreme ultraviolet (EUV) at 13.5 nm ensure a sufficient sensitivity of the
measured light diffraction pattern with regard to the structure details. Obviously, the impact of structure
roughness with amplitudes in the range of a few nanometers can no longer be neglected in the course of the profile
reconstruction. To model line roughness, i.e., line edge (LER) and line width (LWR) roughness, a large number
of finite element (FEM) simulations are performed for domains with large periods, each containing many pairs
of line and space with stochastically chosen widths. These structures are composed of TaN -absorber lines with
an underlying MoSi -multilayer stack representing a typical EUV mask. The resulting mean efficiencies and the
variances of the efficiencies in dependence on different degrees of roughness are calculated. A systematic decrease
of the mean efficiencies for higher diffraction orders along with increasing variances are observed. In particular,
we obtain a simple analytical expression for the bias in the mean efficiencies and the additional uncertainty
contribution stemming from the presence of LER and/or LWR. As a consequence, the bias has to be included
into the model to provide accurate values for the reconstructed critical profile parameters. The sensitivity of the
reconstructed CDs in respect of roughness is demonstrated by using numerous LER/LWR perturbed datasets of
efficiencies as input data for the reconstructions. Finally, the reconstructed critical dimensions are significantly
improved toward the nominal values if the scattering efficiencies are bias-corrected.
The solution of the inverse problem in scatterometry employing deep ultraviolet light (DUV) is discussed, i.e. we
consider the determination of periodic surface structures from light diffraction patterns. With decreasing dimensions
of the structures on photo lithography masks and wafers, increasing demands on the required metrology
techniques arise. Scatterometry as a non-imaging indirect optical method is applied to periodic line structures
in order to determine the sidewall angles, heights, and critical dimensions (CD), i.e., the top and bottom widths.
The latter quantities are typically in the range of tens of nanometers. All these angles, heights, and CDs are the
fundamental figures in order to evaluate the quality of the manufacturing process. To measure those quantities
a DUV scatterometer is used, which typically operates at a wavelength of 193 nm. The diffraction of light by
periodic 2D structures can be simulated using the finite element method for the Helmholtz equation. The corresponding
inverse problem seeks to reconstruct the grating geometry from measured diffraction patterns. Fixing
the class of gratings and the set of measurements, this inverse problem reduces to a finite dimensional nonlinear
operator equation. Reformulating the problem as an optimization problem, a vast number of numerical schemes
can be applied. Our tool is a sequential quadratic programing (SQP) variant of the Gauss-Newton iteration. In
a first step, in which we use a simulated data set, we investigate how accurate the geometrical parameters of an
EUV mask can be reconstructed, using light in the DUV range. We then determine the expected uncertainties
of geometric parameters by reconstructing from simulated input data perturbed by noise representing the estimated
uncertainties of input data. In the last step, we use the measurement data obtained from the new DUV
scatterometer at PTB to determine the geometrical parameters of a typical EUV mask with our reconstruction
algorithm. The results are compared to the outcome of investigations with two alternative methods namely EUV
scatterometry and SEM measurements.
Scatterometry, the analysis of light diffracted from a periodic structure, is a versatile metrology tool for characterizing
periodic surface structures, regarding the critical dimension (CD) and other properties of the surface
profile. For extreme ultraviolet (EUV) masks, only EUV radiation provides direct information on the mask
performance comparable to the operating regime in an EUV lithography tool. With respect to the small feature
dimensions on EUV masks, the short wavelength of EUV is also advantageous since it provides a large number of
diffraction orders from the periodic structures irradiated. We present measurements at a prototype EUV mask
with large fields of periodic lines-space structures using an EUV reflectometer at the Berlin storage ring BESSY
II and discuss the corresponding reconstruction results with respect to their measurement uncertainties. As a
non-imaging indirect optical method scatterometry requires the solution of the inverse problem, i.e., the determination
of the geometry parameters describing the surface profile from the measured light diffraction patterns.
In the time-harmonic case the numerical simulation of the diffraction process for periodic 2D structures can be
realized by the finite element solution of the two-dimensional Helmholtz equation. Restricting the solutions to
a class of surface profiles and fixing the set of measurements, the inverse problem can be formulated as a nonlinear
operator equation in Euclidean space. The operator maps the profile parameters to special efficiencies of
diffracted plane wave modes. We employ a Gauss-Newton type iterative method to solve this operator equation,
i.e., we minimize the deviation of the calculated efficiencies from the measured ones by variation of the geometry
parameters. The uncertainties of the reconstructed geometry parameters depend on the uncertainties of the
input data and can be estimated by statistical methods like Monte Carlo or the covariance method applied to
the reconstruction algorithm. The input data of the reconstruction are very complex, i.e., they consists not only
of the measured efficiencies, but furthermore of fixed and presumed model parameters such as the widths of the
layers in the Mo/Si multilayer mirror beneath the line-space structure. Beside the impact of the uncertainties on
the measured efficiencies, we analyze the influence of deviations in the thickness and periodicity of the multilayer
stack on the measurement uncertainties of the critical dimensions.
The solution of the inverse problem in scatterometry, i.e. the determination of periodic surface structures from light
diffraction patterns, is incomplete without knowledge of the uncertainties associated with the reconstructed surface
parameters. With decreasing feature sizes of lithography masks, increasing demands on metrology techniques arise.
Scatterometry as a non-imaging indirect optical method is applied to periodic line-space structures in order to determine
geometric parameters like side-wall angles, heights, top and bottom widths and to evaluate the quality of the
manufacturing process. The numerical simulation of the diffraction process is based on the finite element solution of the
Helmholtz equation. The inverse problem seeks to reconstruct the grating geometry from measured diffraction patterns.
Restricting the class of gratings and the set of measurements, this inverse problem can be reformulated as a non-linear
operator equation in Euclidean spaces. The operator maps the grating parameters to the efficiencies of diffracted plane
wave modes. We employ a Gauss-Newton type iterative method to solve this operator equation and end up minimizing
the deviation of the measured efficiency or phase shift values from the simulated ones. The reconstruction properties and
the convergence of the algorithm, however, is controlled by the local conditioning of the non-linear mapping and the
uncertainties of the measured efficiencies or phase shifts. In particular, the uncertainties of the reconstructed geometric
parameters essentially depend on the uncertainties of the input data and can be estimated by various methods. We
compare the results obtained from a Monte Carlo procedure to the estimations gained from the approximative covariance
matrix of the profile parameters close to the optimal solution and apply them to EUV masks illuminated by plane waves
with wavelengths in the range of 13 nm.
At PTB a new type of DUV scatterometer has been developed. The concept of the system is very variable, so that many
different types of measurements like e. g. goniometric scatterometry, ellipsometric scatterometry, polarisation
dependent reflectometry and ellipsometry can be performed. The main applications are CD, pitch and edge profile
characterisation of nano-structured surfaces mainly, but not only, on photomasks. Different operation wavelength down
to 193nm can be used. The system is not only a versatile tool for a variety of different at-wavelength metrology
connected with state-of-the-art photolithography. It allows also to adapt and to vary the measurand and measurement
geometry to optimise the sensitivity and the unambiguity for the measurement problem. For the evaluation of the
measurements the inverse diffraction problem has to be solved. For this purpose we developed a special FEM-based
software, which is capable to solve both the direct diffraction problem and the inverse diffraction problem. The latter
can be accomplished using different optimisation schemes. Additionally this software allows also to estimate the quality
of the measured data and the model based measurement uncertainty. This paper gives an overview about the PTB DUV
scatterometer, it's metrological potential and the evaluation methods applied using the software DIPOG2.1.
We discuss numerical algorithms for the determination of periodic surface structures from light diffraction patterns.
With decreasing feature sizes of lithography masks, increasing demands on metrology techniques arise.
Scatterometry as a non-imaging indirect optical method is applied to simple periodic line structures in order to
determine parameters like side-wall angles, heights, top and bottom widths and to evaluate the quality of the
manufacturing process. The numerical simulation of diffraction is based on the finite element solution of the
Helmholtz equation. The inverse problem seeks to reconstruct the grating geometry from measured diffraction
patterns. Restricting the class of gratings and the set of measurements, this inverse problem can be reformulated
as a non-linear operator equation in Euclidean spaces. The operator maps the grating parameters to special
efficiencies of diffracted plane wave modes. We employ a Gauss-Newton type iterative method to solve this operator
equation. The reconstruction properties and the convergence of the algorithm, however, is controlled by the
local conditioning of the non-linear mapping. To improve reconstruction and convergence, we determine optimal
sets of efficiencies optimizing the condition numbers of the corresponding Jacobians. Numerical examples are
presented for "chrome on glass" masks under the wavelength 632.8 nm and for EUV masks.
Resist-surface bound air bubbles have been identified as a possible defect mechanism in immersion lithography. The general expectation is that the bubble will primarily cause local dose reductions, but no detailed simulations on this effect have been published. The work described in this paper is a first attempt to do so: we have simulated the effect of bubbles on 1:1 dense Line/Space patterning. Our results confirm that the major effect of the presence of a bubble is indeed underexposure - or in most cases even non-exposure - of the pattern in the area occupied by the bubble, but it also identifies a few more subtle characteristics of bubble-induced defects which can help identify defects observed on immersion wafers as being caused by a bubble. Apart from the simulation results, we also show a few experimentally observed immersion defects, which we believe are indeed generated by a bubble.