Poul-Erik Hansen

Accounting for PDMS shrinkage when replicating structures

Polydimethylsiloxane (PDMS) is a widely used material for fabrication of microfluidic devices and for replication of micro- and nanotextured surfaces. Shrinkage of PDMS in the fabrication process can lead to leaking devices and poor alignment of layers. However, corrections to the mold master are seldom applied to counteract the shrinkage of PDMS. Also, to perform metrological measurements using replica techniques one has to take the shrinkage into account. Thus we report a study of the shrinkage of PDMS with several different mixing ratios and curing temperatures. The shrinkage factor, with its associated uncertainty, for PDMS in the range 40 to 120 °C is provided. By applying this correction factor, it is possible to replicate structures with a standard uncertainty of less than 0.2% in lateral dimensions using typical curing temperatures and PDMS mixing ratios in the range 1:6 to 1:20 (agent:base).

Comparison of optical methods for surface roughness characterization

We report a study of the correlation between three optical methods for characterizing surface roughness: a laboratory scatterometer measuring the bi-directional reflection distribution function (BRDF instrument), a simple commercial scatterometer (rBRDF instrument), and a confocal optical profiler. For each instrument, the effective range of spatial surface wavelengths is determined, and the common bandwidth used when comparing the evaluated roughness parameters. The compared roughness parameters are: the root-mean-square (RMS) profile deviation (Rq), the RMS profile slope (Rdq), and the variance of the scattering angle distribution (Aq). The twenty-two investigated samples were manufactured with several methods in order to obtain a suitable diversity of roughness patterns.Our study shows a one-to-one correlation of both the Rq and the Rdq roughness values when obtained with the BRDF and the confocal instruments, if the common bandwidth is applied. Likewise, a correlation is observed when determining the Aq value with the BRDF and the rBRDF instruments.Furthermore, we show that it is possible to determine the Rq value from the Aq value, by applying a simple transfer function derived from the instrument comparisons. The presented method is validated for surfaces with predominantly 1D roughness, i.e. consisting of parallel grooves of various periods, and a reflectance similar to stainless steel. The Rq values are predicted with an accuracy of 38% at the 95% confidence interval.

Scatterometry—fast and robust measurements of nano-textured surfaces

Scatterometry is a fast, precise and low cost way to determine the mean pitch and dimensional parameters of periodic structures with lateral resolution of a few nanometer. It is robust enough for in-line process control and precise and accurate enough for metrology measurements. Furthermore, scatterometry is a non-destructive technique capable of measuring buried structures, for example a grating covered by a thick oxide layer. As scatterometry is a non-imaging technique, mathematical modeling is needed to retrieve structural parameters that describe a surface. In this review, the three main steps of scatterometry are discussed: the data acquisition, the simulation of diffraction efficiencies and the comparison of data and simulations. First, the intensity of the diffracted light is measured with a scatterometer as a function of incoming angle, diffraction angle and/or wavelength. We discuss the evolution of the scatterometers from the earliest angular scatterometers to the new imaging scatterometers. The basic principle of measuring diffraction efficiencies in scatterometry has remained the same since the beginning, but the instrumental improvements have made scatterometry a state-of-the-art solution for fast and accurate measurements of nano-textured surfaces. The improvements include extending the wavelength range from the visible to the extreme ultra-violet range, development of Fourier optics to measure all diffraction orders simultaneously, and an imaging scatterometer to measure area of interests smaller than the spot size. Secondly, computer simulations of the diffraction efficiencies are discussed with emphasis on the rigorous coupled-wave analysis (RCWA) method. RCWA has, since the mid-1990s, been the preferred method for grating simulations due to the speed of the algorithms. In the beginning the RCWA method suffered from a very slow convergence rate, and we discuss the historical improvements to overcome this challenge, e.g. by the introduction of Lis factorization rules and the introduction of the normal vector method. The third step is the comparison, where the simulated diffraction efficiencies are compared to the experimental data using an inverse modeling approach. We discuss both a direct optimization scheme using a differential evolution algorithm and a library search strategy where diffraction efficiences of expected structures are collected in a database. For metrology measurements two methods are described for estimating the uncertainty of the fitting parameters. The first method is based on estimating the confidence limits using constant chi square boundaries, which can easily be computed when using the library search strategy. The other method is based on calculating the covariances of all the free parameters using a least square optimization. Scatterometry is already utilized in the semiconductor industry for in-line characterization. However, it also has a large potential for other industrial sectors, including sectors making use of injection molding or roll-2-roll fabrication. Using the library search strategy, the comparison can be performed in ms, making in-line characterization possible and we demonstrate that scatterometry can be used for quality control of injection molded nano-textured plastic samples. With the emerging methods of highly parallel manufacturing of nano-textured devices, scatterometry has great potential to deliver a characterization method for in-line quality control and metrology measurements, which is not possible with conventional characterization techniques. However, there are some open challenges for the scatterometry techniques. These include corrections for measuring on non-ideal samples with a large surface roughness or line-edge roughness and the path towards performing traceable scatterometry measurements.

Fast characterization of moving samples with nano-textured surfaces

Characterization of structures using conventional optical microscopy is restricted by the diffraction limit. Techniques such as atomic force and scanning electron microscopy can investigate smaller structures but are very time consuming. We show that using scatterometry, a technique based on optical diffraction, integrated into a commercial light microscope we can characterize nano-textured surfaces in a few milliseconds. The adapted microscope has two detectors, a CCD camera used to easily find an area of interest and a spectrometer for the measurements. We demonstrate that the microscope has a resolution in the nanometer range for the topographic parameters—height, width, and sidewall angle of a periodic grating—even in an environment with many vibrations, such as a production facility with heavy equipment.

Profile estimation for Pt submicron wire on rough Si substrate from experimental data

An efficient forward scattering model is constructed for penetrable 2D submicron particles on rough substrates. The scattering and the particle-surface interaction are modeled using discrete sources with complex images. The substrate micro-roughness is described by a heuristic surface transfer function. The forward model is applied in the numerical estimation of the profile of a platinum (Pt) submicron wire on rough silicon (Si) substrate, based on experimental Bidirectional Reflectance Distribution Function (BRDF) data.

Joint Research on Scatterometry and AFM Wafer Metrology

Supported by the European Commission and EURAMET, a consortium of 10 participants from national metrology institutes, universities and companies has started a joint research project with the aim of overcoming current challenges in optical scatterometry for traceable linewidth metrology. Both experimental and modelling methods will be enhanced and different methods will be compared with each other and with specially adapted atomic force microscopy (AFM) and scanning electron microscopy (SEM) measurement systems in measurement comparisons. Additionally novel methods for sophisticated data analysis will be developed and investigated to reach significant reductions of the measurement uncertainties in critical dimension (CD) metrology. One final goal will be the realisation of a wafer based reference standard material for calibration of scatterometers.

Investigation of microstructured fiber geometries by scatterometry

Hollow-core photonic bandgap fibers guide light using diffraction rather than total internal reflection as is the case with normal single- mode communications fibers. The fibers consist of a hollow capillary (~19 micrometers in diameter) surrounded by capillary (~4 micrometers in diameter) arranged in a honey-comb like structure. The honey-comb structure scatters light in the core such that light within the bandgap wavelengths cannot escape from the core. However, the bandgap properties greatly depend on the accuracy with which the microstructures can be controlled during the fabrication process. For measuring the geometrical properties of hollow core photonic crystal fibers with a honeycomb cladding structure we use an angular scatterometric setup. For analyzing the experimentally obtained data we rigorously compute the scattering signal by solving Maxwells equations with finite-element methods. This contribution focuses on the numerical analysis of the problem. A convergence analysis demonstrates that we reach highly accurate solutions. Our results show very good qualitative agreement between experimental and numerical results. We furthermore demonstrate concepts for accurately monitoring dimensional parameters in the fiber manufacturing process.

Critical dimension metrology using optical diffraction microscopy

We present an innovative method Optical Diffraction Microscopy (ODM). for the simultaneous measurement of specular and non-specular diffraction patterns of sub-micron periodic structures. A sample is illuminated with broadband light and the diffraction pattern is collected by using a pair of ellipsoidal mirrors, optical fibers and a spectrometer. This method allows for rapid measurements and makes used of the Rigorous Coupled Wave algorithm for data analysis. In the present work the method has been applied to binary and multi-layer sub-micron gratings. A series of binary gratings with periods of 318 nm and 360 nm with different exposure levels of the photoresist were investigated. We succeded in characterize underexposed, ideally exposed and overexposed photoresist grating profiles. The measurements are well-suited to determine the delivered exposure energy density to photoresist gratings. The ODM technique may thus be applied to specify the exposure window and as a feedback in order to adjust the exposure energy density on-line. The homogeneity of a grating on multi-layered substrate has been investigated. Heights and duty cycles ranging from 50 nm to 55 nm and 0.25 to 0.97, respectively, have been found. AFM measurements of the gratings verify the ODM results and demonstrate that the ODM technique can be used to determine grating topology.

Scatterometry reference standards to improve tool matching and traceability in lithographical nanomanufacturing

High quality scatterometry standard samples have been developed to improve the tool matching between different scatterometry methods and tools as well as with high resolution microscopic methods such as scanning electron microscopy or atomic force microscopy and to support traceable and absolute scatterometric critical dimension metrology in lithographic nanomanufacturing. First samples based on one dimensional Si or on Si3N4 grating targets have been manufactured and characterized for this purpose. The etched gratings have periods down to 50 nm and contain areas of reduced density to enable AFM measurements for comparison. Each sample contains additionally at least one large area scatterometry target suitable for grazing incidence small angle X-ray scattering. We present the current design and the characterization of structure details and the grating quality based on AFM, optical, EUV and X-Ray scatterometry as well as spectroscopic ellipsometry measurements. The final traceable calibration of these standards is currently performed by applying and combining different scatterometric as well as imaging calibration methods. We present first calibration results and discuss the final design and the aimed specifications of the standard samples to face the tough requirements for future technology nodes in lithography.

Modeling surface imperfections in thin films and nanostructured surfaces

Accurate scatterometry and ellipsometry characterization of non-perfect thin films and nanostructured surfaces are challenging. Imperfections like surface roughness make the associated modelling and inverse problem solution difficult due to the lack of knowledge about the imperfection on the surface. Combining measurement data from several instruments increases the knowledge of non-perfect surfaces. In this paper we investigate how to incorporate this knowledge of surface imperfection into inverse methods used in scatterometry and ellipsometry using the Rigorous Coupled Wave Analysis. Three classes of imperfections are examined. The imperfections are introduced as periodic structures with a super cell periods ten times larger than the simple grating period. Two classes of imperfections concern the grating and one class concern the substrate. It is shown that imperfections of a few nanometers can severely change the reflective response on silicon gratings. Inverse scatterometry analyses of gratings with imperfection using simulated data with white noise have been performed. The results show that scatterometry is a robust technology that is able to characterize grating imperfections provided that the imperfection class is known.