Indirect optical methods like ellipsometry or scatterometry require an optical model to calculate the response of the system, and to fit the parameters in order to minimize the difference between the calculated and measured values. The most common problem of optical modeling is that the measured structures and materials turn out to be more complex in reality than the simplified optical models used as first attempts to fit the measurement. The complexity of the optical models can be increased by introducing additional parameters, if they (1) are physically relevant, (2) improve the fit quality, (3) don't correlate with other parameters. The sensitivity of the parameters can be determined by mathematical analysis, but the accuracy has to be validated by reference methods. In this work some modeling and verification aspects of ellipsometry and optical scatterometry will be discussed and shown for a range of materials (semiconductors, dielectrics, composite materials), structures (damage and porosity profiles, gratings and other photonic structures, surface roughness) and cross-checking methods (atomic force microscopy, electron microscopy, x-ray diffraction, ion beam analysis). The high-sensitivity, high-throughput, in situ or in line capabilities of the optical methods will be demonstrated by different applications.
Scatterometry is a common tool for the dimensional characterization of periodic nanostructures. In this paper we compare measurement results of two different scatterometric methods: a goniometric DUV scatterometer and a coherent scanning Fourier scatterometer. We present a comparison between these two methods by analyzing the measurement results on a silicon wafer with 1D gratings having periods between 300 nm and 600 nm. The measurements have been performed with PTB’s goniometric DUV scatterometer and the coherent scanning Fourier scatterometer at TU Delft. Moreover for the parameter reconstruction of the goniometric measurement data, we apply a maximum likelihood estimation, which provides the statistical error model parameters directly from measurement data.
Optical techniques have been intensively developed for many decades in terms of both experimental and modeling capabilities. In spectroscopy and scatterometry material structures can be measured and modeled from the atomic (binding configurations, electronic band structure) through nanometer (nanocrystals, long range order) to micron scales (photonic structures, gratings, critical dimension measurements). Using optical techniques, atomic scale structures, morphology, crystallinity, doping and a range of other properties that can be related to the changes of the electronic band structure can most sensitively be measured for materials having interband transition energies in the optical photon energy range. This will be demonstrated by different models for the dielectric function of ZnO, a key material in optoelectronics and in numerous other fields. Using polarimetry such as spectroscopic ellipsometry, sub-nanometer precision has long been revealed for the thickness of optical quality layers. The lateral resolution of spectroscopic ellipsometry is limited (> 50 μm) by the use of incoherent light sources, but using single-wavelength imaging ellipsometry, a sub-micron lateral resolution can be reached. In case of sub-wavelength structures, the morphology (of e.g. porous or nanocrystalline materials) can be characterized using the effective medium theory. For structure sizes comparable to the wavelength, scatterometry is applied in a broad versatility of configurations from specular to angle resolved, from coherent to incoherent, from monochromatic to spectroscopic, from reectometric to polarimetric. In this work, we also present an application of coherent Fourier scatterometry for the characterization of periodic lateral structures.
Incoherent Optical Scatterometry (IOS) is widely used in semiconductor industry in applications related to optical
metrology particularly in grating reconstruction. Recently, Coherent Fourier Scatterometry (CFS) has emerged as a
strong alternative to the traditional IOS under suitable condition. When available, phase information is an added
advantage in CFS to complement the intensity data. Phase information in the scattered far field is dependent on the
structure and the composition of the grating. We derive and discuss the phase information accessible through the CFS.
Phase difference between the diffracted orders is computed and the polarization dependent phase sensitivity of the
grating parameters are discussed. The results are rigorously simulated and an experimental implementation of CFS
demonstrates the functionality of the method.
Measurement techniques to determine the aberration of an optical system, by obtaining through-focus intensity
images that are produced when the object is a point source at infinity, are shown. The analysis of the aberrations
is made using the extended version of the Nijboer-Zernike diffraction theory. This theory provides a semi
analytical solution of the Debye diffraction integral and thus a direct relation between the intensity distribution
of the field at the focal region and the exit pupil of the optical system.
Incoherent Optical Scatterometry (IOS) is a well-established metrology technique in the semiconductor industry to
retrieve periodic grating structures with high accuracy from the signature of the diffracted optical far field. With
shrinking dimensions in the lithography industry, finding possible improvements in wafer metrology is highly desirable.
The grating is defined in terms of a finite number of geometrical shape parameters (height, side-wall angles, midCD
etc.). In our method the illumination is a scanning focused spot from a spatially coherent source (laser) within a single
period of the grating. We present a framework to study the increment in sensitivity of Coherent Fourier Scatterometry
(CFS) with respect to the IOS. Under suitable conditions, there is a more than fourfold enhancement in sensitivity for
grating shape parameters using CFS. The dependence of scanning positions on the sensitivity analysis is also highlighted.
We further report the experimental implementation of a Coherent Fourier Scatterometer. The simulated and
experimental far fields are compared and analyzed for the real noise in the experimental configuration.
The technology path to produce low cost microinterferometric heads in plastic and the optical methods for quality
investigations of these elements are presented. Specifically the interferometric and photoelastic tomography methods,
applied for the 3D studies of refractive index (n) and birefringence (B) in photonics components replicated by means of
hot embossing (HE) technology, are investigated. The enhanced automated measurement and data analysis procedures
are described and the experimental results obtained for micro-objects working in transmission are given. Also the
methodology to combine the tomographic data for full characterization of internal structure of 3D photonics elements is
provided. The samples under test are massive waveguide microinterferometerers in the form of cuboids produced by hot
embossing process characterized by a variety of parameters. The systematic tomographic studies of 3D distribution of n
and B provided important information for extending knowledge about the process and optimization hot embossing
technology. The tomographic measurements are supported by measurements of top and side walls profile and roughness.
Multimode laser emission is observed in a polymer optical fiber doped with a mixture of rhodamine 6G and rhodamine B dyes. Tuning of laser emission is achieved by using the mixture of dyes due to the energy transfer occurring from donor molecule (rhodamine 6G) to acceptor molecule (rhodamine B). The dye doped polymethylmethacrylate (PMMA) based polymer optical fiber is pumped axially at one end of the fiber using 532nm pulsed laser beam from an Nd: YAG laser and the fluorescence emission is collected from the other end. At low pump energy levels, fluorescence emission is observed. When the energy is increased beyond a threshold value, laser emission occurs with a multimode structure. The optical feedback for the gain medium is provided by the cylindrical surface of the optical fiber which acts as a cavity. This fact is confirmed by the mode spacing dependence on the diameter of the fiber.