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Spectroscopic polarization measurement and control using channeled spectrum has several unique features and is useful for various spectroscopic instruments. It utilizes the strong dispersion characteristics in polarization retardation of high-order retarders so that the polarization modulation can be made without using mechanical or active elements for polarization modulation. In this presentation, we describe its principle, basic features, and several applications including a spectroscopic ellipsometer and ultrafast rotations of beam profile and polarization.

Utilizing flow cytometry to monitor progress of bulk biochemical reactions and concentration of chemical species normally relies on the utilization of cells carrying intrinsic fluorescence or modified beads. We present a method for a simple measurement of the fluorescent marker molecule fluorescein and GFPuv in bulk solutions with high sensitivity using a CytoFLEX flow cytometer and without the need for modified beads. Polystyrene beads were used to trigger measurements based on their high scatter signal, to detect the fluorescence signal from two different fluorophores present in the sample solution. We report sensitivities of 33 pg/mL for fluorescein and 50 ng/mL for GFPuv. This method is comparable in sensitivity to a typical spectrometric fluorescence assay tested with fluorescein, and approximately ten times more sensitive for the measurement of GFPuv. PEG was added to the sample at a low concentration of 0.001% (w/v) to block unspecific GFPuv binding to the beads. The method was further applied to measure the GFPuv concentration in crude cell lysate samples used for cell free protein expression. An advantage of this method over spectrometric assays is the ability to differentiate signal subpopulations in the sample based on their individual fluorescence intensities.

Background: Scatterometry is a fast, indirect and non-destructive optical method for quality control in the production of lithography masks. To solve the inverse problem in compliance with the upcoming need for improved accuracy, a computationally expensive forward model has to be defined which maps geometry parameters to diffracted light intensities. Aim: To quantify the uncertainties in the reconstruction of the geometry parameters, a fast to evaluate surrogate for the forward model has to be introduced. Approach: We use a non-intrusive polynomial chaos based approximation of the forward model which increases speed and thus enables the exploration of the posterior through direct Bayesian inference. Additionally, this surrogate allows for a global sensitivity analysis at no additional computational overhead. Results: This approach yields information about the complete distribution of the geometry parameters of a silicon line grating, which in return allows to quantify the reconstruction uncertainties in the form of means, variances and higher order moments of the parameters. Conclusion: The use of a polynomial chaos surrogate allows to quantify both parameter influences and reconstruction uncertainties. This approach is easy to use since no adaptation of the expensive forward model is required., arXiv admin note: substantial text overlap with arXiv:1910.14435

Especially in metrology and geodesy, but also in many other disciplines, the solution of overdetermined linear systems of the form A x ≈ b with individual uncertainties not only in b but also in A is an important task. The problem is known in literature as weighted total least squares. In the most general case, correlations between the elements of A , b exist as well. The problem becomes more complicated and can—except for special cases—only be solved numerically. While the formulation of this problem and even its solution is straightforward, its implementation—when the focus is on reliability and computational costs—is not. In this paper, a robust, fast, and universal method for computing the solution of such linear systems as well as their covariance matrix is presented. The results were confirmed by applying the method to several special cases for which an analytical or numerical solution is available. If individual coefficients can be considered to be free of errors, this can be taken into account in a simple way. An implementation of the code in MATLAB is provided.

Spectroscopic ellipsometry is a versatile tool to measure dimensional or optical parameters of surface layers or surface structures. The determination of these parameters requires to solve an inverse problem. This is achieved by a fitting procedure, where a merit function is optimized. This merit function compares simulated with measured polarization quantities for each measurement configuration, i. e. for each wavelength and angle of incidence. For the simulation of unstructured samples Fresnel-equations can be used, while for structured surfaces the Maxwells equations must be solved using so-called Maxwell-solvers. For depolarizing samples Mueller ellipsometry must be used, because only the Mueller-stokes formalism is capable to describe depolarization. However, in common approaches to evaluate Mueller matrix measurements depolarization is treated in a nonoptimal way, which leads to inadequate measurement uncertainty estimations and in the worst case may lead to systematic measurement errors. Especially for surfaces with strong depolarization such as rough or textured surfaces this is a problem. To treat these issues, we developed an improved analysis method to attain reliable sample parameters and reliable and mathematically well-founded uncertainty estimations from Mueller ellipsometry measurements. While deterministic non-depolarising samples can be fully described within the well-known Jones formalism and can be simulated by Fresnel- or Maxwell-solvers, a complete simulation of depolarizing samples would require very high computational expenses which are too elaborate or even impossible in practice. Thus the question arises, how to treat depolarization in the optimization process. Commonly used merit functions treat it as a residual error, which is minimized and accept the fit solution with the smallest overall depolarization as the best approximation. However, depolarization is a sample property, which must not be minimized. Therefore, instead we use the depolarization to derive a weight-factor for each residual contribution to the merit-function. We will present the underlying mathematics. The evolved theory is applicated on measurement data obtained with a Sentech SE 850 system. The Mueller-matrices for each measurement configuration are computed from an overdetermined system of raw data achieved with analyzer-scans at discrete polarizer-steps (step-scan-mode). Thus the raw measurement data can additionally be exploited to get statistical information to the measured Mueller matrices and included in the merit function. Embedded into a Bayesian approach the best-fit values and their uncertainties are determined from the posterior distribution in a much more realistic and reliable way. Applied on both virtual and real measurement data, we demonstrate the advantages of this new method and compare the results with different standard analysis methods.

Accurate metrology of nanostructures gains more and more importance and for efficiency reasons optical methods play a significant role here. Unfortunately, conventional optical microscopy is subject to the well-known resolution limit. The necessity to resolve objects smaller than this limit led to the development of superresolution methods which however are barely used in metrology for practical reasons. Non-imaging indirect optical methods like scatterometry and ellipsometry however are not limited by diffraction and are able to determine the critical dimensions of nanostructures. We investigate the application of different approaches for specifically manipulated near-fields in Mueller matrix ellipsometry to achieve an enhanced sensitivity for polarization based sub-wavelength topological information. To this end, we present first numerical simulations of these approaches. To examine the relationship between structural properties and Mueller matrix elements we designed individual structures based on geometrical shapes of varying parameters as well as small arrays. They are realized by lithography as holes in PMMA resist. First, we characterize SEM images of the structures to validate the fabrication process. Numerical simulations of the Mueller matrices of the structures by finite element method are discussed. Results indicate that conventional Mueller matrix ellipsometry alone is unsuitable but the extension to imaging Mueller matrix microscopy is promising for the characterization of sub-wavelength features.

Scatterometry is a fast, indirect and nondestructive optical method for the quality control in the production of lithography masks. Geometry parameters of line gratings are obtained from diffracted light intensities by solving an inverse problem. To comply with the upcoming need for improved accuracy and precision and thus for the reduction of uncertainties, typically computationally expansive forward models have been used. In this paper we use Bayesian inversion to estimate parameters from scatterometry measurements of a silicon line grating and determine the associated uncertainties. Since the direct application of Bayesian inference using MarkovChain Monte Carlo methods to physics-based partial differential equation (PDE) model is not feasible due to high computational costs, we use an approximation of the PDE forward model based on a polynomial chaos expansion. The expansion provides not only a surrogate for the PDE forward model, but also Sobol indices for a global sensitivity analysis. Finally, we compare our results for the global sensitivity analysis with the uncertainties of estimated parameters.

There are some commonly-used optimization techniques for the analysis of measured data in spectroscopic Mueller matrix ellipsometry (MME) used, for example, to calculate the layer thicknesses of samples under test. Concentrating on the metrological aspects of MME, we identified a non-optimal treatment of depolarization in all these techniques. We therefore recently developed an improved optimization method to adequately take depolarization in MME into account. In a further step, we also included statistical measurement noise and derived a likelihood function, which enabled us to apply both the maximum likelihood method and Bayesian statistics as well as the Bayesian information criterion for data evaluation. In this paper we concentrate on the application of this new method to measurements of SiO2-layer thicknesses on silicon. With a state-of-the-art SENTECH SENresearch 4.0 Mueller ellipsometer, we measured standard samples of different SiO2-layer thicknesses, whose calibrated thicknesses were between about 6 nm and 1000 nm. The MME results were compared to the calibration data. For all samples, an SiO2-SiO double-layer model turned out to be optimal. The measured total oxide layer thicknesses matched excellently with the calibration values, within the estimated range of uncertainties. All the results are presented here. This is the first comparison with traceable reference measurements demonstrating the validity of our novel MME analysis method.

In this paper, we focus on the metrological aspects of spectroscopic Mueller ellipsometry—i.e. on the uncertainty estimation of the measurement results. With the help of simulated Mueller matrices, we demonstrate that the commonly used merit functions do not return the correct uncertainty for the measurand under consideration (here shown for the relatively simple case of the geometrical parameter layer thickness for the example system of a SiO2 layer on a Si substrate). We identify the non-optimal treatment of measured and sample- induced depolarization as a reason of this discrepancy. Since depolarization results from sample properties in combination with experimental parameters, it must not be minimized during the parameter fit. Therefore, we propose a new merit function treating this issue differently: It implicitly uses the measured depolarization as a weighting parameter. It is very simple and computationally cheap. It compares for each wavelength the measured Jones matrix elements to Cloude’s covariance matrix: ∼ ∑ λ j sim, λ † H meas, λ + j sim, λ . Moreover, an extension will be presented which allows us to include the measurement noise into this merit function. With this, reliable statistical uncertainties can be calculated. Except for some pre-processing of the raw data, there is no additional computational cost.

For numerous applications in science and engineering, the development of technologies for assembling and manipulating macro-, micro-, and nano-objects by means of laser light is of high interest. Most of these attractive forces require dielectric particles they can act on. In recently published papers, a negative light pressure was predicted which acts on metallic bodies if these are separated by a subwavelength slit and which arises from surface plasmon interaction between the metallic bodies1,2. An experimental demonstration of this force has not yet been carried out. First theoretical calculations showed that, for example, a laser power of 100 mW which is fully absorbed in the slit of a laser with a wavelength of 1550 nm would, in a slit having a width of half the wavelength, generate a force of about 1 nN. However, this is roughly three times the force of the radiation pressure of about 0.33 nN. In this work, we present an experimental setup to measure this force, together with results of refined theoretical calculations and with preliminary results achieved with the experimental setup.

In recent works, a novel light-induced attractive force was predicted between two metal plates. This force arises by the interaction of surface plasmons which are excited at the metal when a transverse magnetic mode propagates through a subwavelength slit between two metal bodies. In this paper, the analytical and numerical calculations of this magnetic field are presented for the perfect metal and for gold. The amplitude and the phase transient curves between the known limiting cases of narrow and wide slits compared to the wavelength are found. The curve is shown to oscillate due to the emergence of new waveguide modes. The analytic solution for the perfect metal is in agreement with the computation for gold by means of the finite element method. The simple asymptotic formula for the light-induced attractive force is found in the limit of a narrow slit.

The quantification of metabolite leakage from damaged mammalian cells to the surrounding medium is of high interest for the processing of samples for metabolomic analysis. It is also of relevance to know the typical time span which is required for a promoted metabolite release through a selectively permeabilized cell membrane. The real-time observation of such a process is difficult since small metabolites cannot be observed directly by optical methods and other more indirect assays can disturb the metabolite concentration itself. However, the diffusion based loss of metabolites from the cytoplasm can be predicted on the basis of reference measurements taken from an easy-to-detect molecule with known diffusion coefficient. In this work, we use green fluorescent protein (GFP) as a marker and model its release from damaged cells using the finite-element method. A correlation between the disrupted membrane area fraction, A d , the distribution of membrane ruptures and the rate of GFP efflux, k e , has been established. k e has been determined experimentally for Chinese hamster ovary cells, which have been damaged mechanically by passage through a micronozzle geometry in a microfluidic system. The immediate GFP release downstream of the micronozzles has been observed in real-time and the corresponding membrane damage has been predicted. On this basis, we calculated the expected times required for the drainage of freely diffusable cytosolic glucose and found a loss of ≈90% within 1 s for a disrupted membrane area fraction of ≈5%. Hence, even minimal membrane damage would lead to a rapid loss of cytosolic metabolites by diffusion unless membrane resealing processes take place.

One of the key objectives of systems biology is to study and control biological processes in terms of interactions of components at different molecular levels. Advances in genome sequencing, transcriptomics and proteomics have paved the way for a systemic analysis of cellular processes at gene and protein levels. However, tools are still missing for a reliable and systemic analysis of the small molecules inside cells, the so-called metabolome. Due to the generally very low concentration, high turn-over rate and chemical diversity of metabolites their quantification under physiological, in vivo and dynamic conditions presents major challenges and the missing link for a real systems biology approach on the way from genome to cellular function. To this end, microfluidics can play an important role owing to its unique characteristics such as highly spatial and temporal resolution of sample treatment and analysis. Despite impressive progresses in microtechnology in recent years, many of the microfluidic studies or devices remain at the level of proof-of-principle and have been seldom applied to the real world of metabolomic analysis. In this review article, we first present the major obstacles and challenges for determining in vivo metabolite dynamics in complex biological systems. The progresses in microfluidics, their characteristics and possible applications to solving some of the compelling problems in metabolomic analysis are then discussed. Emphases are put on pinpointing the deficits of the presently available devices and technologies and directions for further development to fulfill the special need of systems biology.

We report the initial results of a recent bilateral comparison of linewidth or critical dimension (CD) calibrations on photomask line features between two national metrology institutes (NMIs): the National Institute of Standards and Technology (NIST) in the United States and the Physikalisch-Technische Bundesanstalt (PTB) in Germany. For the comparison, a chrome on glass (CoG) photomask was used which has a layout of line features down to 100 nm nominal size. Different measurement methods were used at both institutes. These included: critical dimension atomic force microscopy (CD-AFM), CD scanning electron microscopy (CD-SEM) and ultraviolet (UV) transmission optical microscopy. The measurands are CD at 50 % height of the features as well as sidewall angle and line width roughness (LWR) of the features. On the isolated opaque features, we found agreement of the CD measurements at the 3 nm to 5 nm level on most features – usually within the combined expanded uncertainties of the measurements.

In this work, we illustrate the benefits and problems of mathematical modelling and effective numerical algorithms to determine the diffraction of light by periodic grating structures. Such models are required for reconstruction of the grating structure from the light diffraction patterns. With decreasing structure dimensions on lithography masks, increasing demands on suitable metrology techniques arise. Methods like scatterometry as a non-imaging indirect optical method offer access to the geometrical parameters of periodic structures including pitch, side-wall angles, line heights, top and bottom widths. The mathematical model for scatterometry is based on the Helmholtz equation derived as a time-harmonic solution of the Maxwell equations. It determines the incident and scattered electric and magnetic fields, which fully specify the light propagation in a periodic two-dimensional grating structure. For numerical simulations of the diffraction patterns, a standard finite element method (FEM) or a generalized finite element method (GFEM) is used for solving the elliptic Helmholtz equation. In a first step, we performed systematic forward calculations for different varying structure parameters to evaluate the applicability and sensitivity of different scatterometric measurement methods. Furthermore our programs include several iterative optimization methods for reconstructing the geometric parameters of the grating structure by the minimization of a functional. First reconstruction results for different test data sets are presented.

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 Si 3 N 4 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.

The intersubband relaxation of holes in p-type modulation-doped Si 1− x Ge x /Si multiple quantum wells is studied both experimentally and theoretically. Pump–probe experiments with 150-fs midinfrared pulses yield a lifetime of holes in the second heavy-hole subband of only 250 fs for 4.4-nm wide wells with x =0.5. This short lifetime is caused by interaction with phonons via the optical deformation potential. Calculations of hole–phonon scattering agree very well with the experimental results. The calculations show that longer heavy-hole lifetimes are possible by increasing the Ge content and the well widths.

We report on an experimental and theoretical study of intersubband relaxation of holes in p-type modulation-doped Si 1− x Ge x /Si multiple quantum wells. The ultrafast hole dynamics is studied in pump–probe experiments with 150 fs mid-infrared pulses. For 4.4 nm wide wells ( x =0.5) the lifetime of holes in the second heavy hole subband is only 250 fs due to rapid emission of optical phonons via the deformation potential interaction. Model calculations of hole–phonon scattering give an almost identical value and point to the crucial role of cascaded scattering via an intermediate subband with light-hole-split-off symmetry.

We present the first study of ultrafast hole dynamics after resonant intersubband excitation in a quasi-two-dimensional semiconductor. p-type Si0.5Ge 0.5/Si multiple quantum wells are studied in pump-probe experiments with 150 fs midinfrared pulses. Intersubband scattering from the second heavy-hole back to the first heavy-hole subband occurs with a time constant of 250 fs, followed by intrasubband carrier heating within 1 ps. Such processes give rise to a strong reshaping of the intersubband absorption line, which is accounted for by calculations of the subband structure, optical spectra, and hole-phonon scattering rates.

According to the International Technology Roadmap for Semiconductors (ITRS) the semiconductor industry will start to apply Extreme Ultraviolet (EUV) Lithography for printing high-end electronic circuits within the next few years. For the critical dimensional structure parameters like CD, sidewall angle and line edge roughness (LER) besides SEM also atomic force microscopy (AFM) and scatterometry will be important metrology methods.

At PTB we investigate the prospects of scatterometric methods for quantitative dimensional metrology of periodic micro- and nanostructures. Commonly applied approximations and simplifications may lead to contributions to the measurement uncertainty or even to systematic measurement errors. Here we present a short overview about the main effects connected with these simplifications. In particular we present numerical investigations of the influence of a finite beam size on the scatterometry results. The results indicate, that an impact of the finite beam size becomes significant only for tightly focused beams with a beam waist radius wo smaller than 10 μm.

In this contribution we demonstrate goniometric scatterometry measurements of gratings with linewidths down to 25 nm on silicon wafers with an inspection wavelength of 266 nm. For each sample, measurements have been performed in four different configurations and the obtained data have been evaluated in parallel. As results we present the reconstruction of the complete cross-section profile. We introduce a novel geometry parameterization which overcomes some limitations of the default parameterization. A co-variance analysis of the parameters is offered to indicate the soundness of the results. A qualitative comparison with cross-section scanning electron microscope (SEM) images shows excellent agreement.

Supported by the European Commission and EURAMET, a consortium of 10 participants from national metrology institutes, universities and companies has recently started a joint research project with the aim of overcoming current challenges in optical scatterometry for traceable linewidth metrology and to establish scatterometry as a traceable and absolute metrological method for dimensional measurements. This requires a thorough investigation of the influence of all significant sample, tool and data analysis parameters, which affect the scatterometric measurement results. For this purpose and to improve the tool matching between scatterometers, CD-SEMs and CD-AFMs, experimental and modelling methods will be enhanced. The different scatterometry methods will be compared with each other and with specially adapted atomic force microscopy (AFM) and scanning electron microscopy (SEM) measurement systems. 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. To transfer traceability to industrial applications of scatterometry an important step and one final goal of this project is the realisation of different waferbased reference standard materials for calibration of scatterometers. The approaches to reach these goals and first design considerations and preliminary specification of the scatterometry standards are presented and discussed.

Scatterometry is frequently used as a non-imaging indirect optical method to reconstruct the critical dimensions (CD) of periodic nanostructures. A particular promising direction is EUV scatterometry with wavelengths in the range of 13 – 14 nm. The conventional approach to determine CDs is the minimization of a least squares function (LSQ). In this paper, we introduce an alternative method based on the maximum likelihood estimation (MLE) that determines the statistical error model parameters directly from measurement data. By using simulation data, we show that the MLE method is able to correct the systematic errors present in LSQ results and improves the accuracy of scatterometry. In a second step, the MLE approach is applied to measurement data from both extreme ultraviolet (EUV) and deep ultraviolet (DUV) scatterometry. Using MLE removes the systematic disagreement of EUV with other methods such as scanning electron microscopy and gives consistent results for DUV.

The lysis of mammalian cells is an essential part of different lab-on-a-chip sample preparation methods, which aim at the release, separation, and subsequent analysis of DNA, proteins, or metabolites. Particularly for the analysis of compartmented in vivo metabolism of mammalian cells, such a method must be very fast compared to the metabolic turnover-rates, it should not affect the native metabolite concentrations, and should ideally leave cell organelles undamaged. So far, no such a method is available. We have developed a microfluidic system for the effective rapid mechanical cell disruption and established a mathematical model to describe the efficiency of the system. Chinese hamster ovary (CHO) cells were disrupted with high efficiency by passing through two consecutive micronozzle arrays. Simultaneous cell compression and shearing led to a disruption rate of ≥90% at a sample flow rate of Q = 120 μL min(-1) per nozzle passage, which corresponds to a mean fluid velocity of 13.3 m s(-1) and a mean Reynolds number of 22.6 in the nozzle gap. We discussed the problem of channel clogging by cellular debris and the resulting flow instability at the micronozzle arrays. The experimental results were compared to predictions from Computational Fluid Dynamics (CFD) simulations and the critical energy dissipation rate for the disruption of the CHO cell population with known size distribution was determined to be 4.7 × 10(8) W m(-3). Our model for the calculation of cell disruption on the basis of CFD-data could be applied to other microgeometries to predict intended disruption or undesired cell damage.

Previous work has shown that the reconstruction of geometric parameters describing the profile of an attenuated phase shift (MoSi) photomask is possible by a least-square minimization of the difference between measurement data and simulation results. Modelling work on other related systems, in particular EUV scatterometry, has revealed a strong influence of the uncertainties assigned to the input data. Their choice may introduce a systematic bias to the determination of the reconstructed geometric quantities like line height, top- and bottom CDs or side-wall angles. Here we employ a maximum likelihood estimation (MLE) to obtain the profile parameters as well as consistent uncertainty estimates for the input data. The method is applied to a set of goniometric scatterometry measurements at a wavelength of 193nm on a state-of-the-art MoSi mask.

We have measured far field diffraction patterns of different diffractive optical elements at an illumination wavelength of 193 nm using a new type of goniometric DUV (deep ultraviolet) scatterometer, which has been developed and set up recently at the PTB, the national metrology institute of Germany. This system offers both a high dynamic range and angular resolution. The scatterometer is especially suitable to analyse weak background light like stray light and local variations of the diffraction patterns over the DOEs (diffractive optical element). The measurement results are compared with measurements using a CCD (charge-coupled device)-based imaging DOE measurement system from Carl Zeiss SMT. An excellent agreement is demonstrated.

Scatterometry is a common technique for the characterization of nano-structured surfaces. The goal is to establish scatterometry as a traceable and absolute metrological method for dimensional measurements. Scatterometry is an indirect measuring method. There are three aspects to be investigated for a proper estimation of the measurement uncertainties. Firstly, the measured optical properties will have measurement uncertainties. The optimization theory provides well-proven algorithms to propagate the uncertainties of the input parameters to the output, using covariance or Monte Carlo methods. Secondly, it must be assured that the model represents the measurement object sufficiently well. Due to the large number of parameters it takes to model a real object, it is not possible to simultaneously determine all of them from the measured data. Therefore, a priori knowledge about reasonable values for certain model parameters and their associated variances is needed. Their impact on the uncertainties of the reconstructed parameters describing the nano-structured surface has to be considered too. Thirdly, there are assumptions in the model which are inherent properties of the mathematical methods used. The assumption that the structures are periodic over a sufficiently large area, i.e. the measurement field, is of the most importance. Line-edge or line-width roughness are obviously effects disturbing the periodicity and the corresponding uncertainty contribution can be derived by an analytical approach to estimate their influence on the diffracted intensities. In our example the latter contribution is the dominant one.

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.

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.

To test the applicability of scatterometry on EUV masks we measured a prototype EUV mask both with an EUV scatterometer and a conventional scatterometer operated at 193 nm and compared the results with AFM and CD-SEM measurements provided to us by the mask supplier. The results of both CD-SEM and EUV- and DUV scatterometry show a quite good agreement in linearity despite constant CD offsets for these different metrology tools. The influences of the multilayer and Si capping layer on top of the multilayer thickness on EUV scatterometry results have been modelled with the help of FEM based simulations. A strong correlation has been found between the thickness of the capping layer and the sidewall angle. In general these results demonstrate the applicability both of EUV and DUV scatterometry for the characterisation of absorber structures on EUV masks. The application of DUV scatterometry allows to omit any influence from multilayer features and is only sensitive to the absorber structure. In this way EUV and DUV scatterometry complement each other for metrology on EUV masks. For applications in process optimisation and in process control the use of a conventional VIS/DUV-scatterometer may be sufficient in many cases.

Today, various types of high resolution dimensional metrology instrumentation are in use for a quantitative characterisation of micro- and nanostructures. Although sophisticated ultra high resolution microscopic techniques like SEM and AFM are available, optical methods like microscopy and scatterometry are still of interest and are important because they are non-destructive, fast and have a good in-line capability. At PTB different optical tools are used for high-resolution metrology. Our standard instrument for CD metrology is a special UV transmission microscope. A new 193nm microscope is currently under development which will meet future requirements at least for the 32nm node as specified in the ITRS roadmap. A special alternating grazing incidence dark field microscope is used to measure the width of single features down to 100nm. For grating structures, we developed an optical diffractometer for pitch calibrations with an uncertainty down to 10 pm. Recently we realised a DUV scatterometer and ellipsometer capable to measure accurately CD, edge profile, layer thickness, and optical parameters. A versatile EUV scatterometer can be used to characterise absorber structures e. g. on EUV photomasks. For accurate measurements a thorough modelling on the basis of rigorous diffraction calculation is essential, which accounts for both polarisation effects and the 3D geometry of the structures. We use the rigorous coupled wave analysis (RCWA) method and the finite elements (FEM) method. We present an overview of PTB's current and future activities in optical high-resolution metrology and how these systems compare to ultra-high resolution microscopy like SEM or AFM.

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. For the evaluation of the measurements the inverse diffraction problem has to be solved. For this purpose a special FEM-based software has been developed, which is capable to solve both the direct diffraction problem and the inverse diffraction problem. The latter can be accomplished using different optimisation schemes. To test both our new scatterometer and the newly developed evaluation software we started systematic comparative CD and edge profile measurements on a state of the art MoSi phase shift mask. In this paper first results are presented and compared with results of a commercial scatterometer.

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 investigated the potential, applicability, and advantages of DUV scatterometry including DUV ellipsometry for the dimensional characterisation of the absorber structures on EUV photomasks. By means of numerical investigations on the basis of rigorous diffraction calculations we demonstrate the sensitivity of DUV scatterometry with regard to dimensions and geometry of the absorber structures. Further we show, that in contrast to at-wavelength scatterometry in the EUV scatterometry in the DUV spectral range is nearly insensitive to perturbations of the reflecting MoSi multilayer. As for EUV scatterometry the separation of absorber structure and multilayer parameters is sometimes difficult the application of DUV scatterometry allows for an easy separation. It is further on verified, that for this reason a quite good reconstruction of geometry and size of the absorber structures from measured data is possible. Finally we prove the sensitivity of DUV ellipsometric measurements, a feature, which is not (yet) available in the EUV spectral range. Because of these results we estimate DUV scatterometry to be an excellent metrology method for in-line monitoring and process optimization in the fabrication process of EUV masks.

Measurement and control of edge profiles and edge angles is increasingly important in advanced lithography. Especially for critical dimension metrology a sophisticated multi-dimensional shape metrology is highly beneficial. Different types of dimensional metrology instrumentation are in use today for edge profile and edge angle measurement. While destructive cross section SEM measurements often serve as reference, AFM and optical scatterometry systems are commonly used for day-to-day or in-line control. Due to the limitations of these metrology systems (AFM: slow, scatterometry: only integral measurements of periodic structures), the evaluation and modelling of top down SEM images is increasingly considered, too. At the PTB both SEM and AFM as well as optical scatterometry are applied for edge angle and/or edge profile metrology, supported by optical transmission microscopy. At the PTB we have realised a new DUV hybrid scatterometer for measurements over the full range of 6025 format masks which combines essential elements of a reflectometer, an ellipsometer, and a diffractometer. In addition to scatterometric measurements this set-up allows to measure the complete Muller-matrix including transmission, polarisation and depolarisation. This new set-up will be presented in detail. Finally we study the possibilities of evaluating high resolution top down SEM images to determine edge angles. The potential of edge angle evaluation using these new analysis procedures will be discussed. We present an overview of the PTB measurement capabilities with an emphasis on newly developed metrology methods and systems.

With decreasing critical dimensions (CD) on lithography masks, increasing demands on CD metrology techniques come along. Already today the results of the three standard methods for CD measurements currently used, atomic force microscopy (AFM), scanning electron microscopy (SEM), and optical microscopy, typically do not yield the same results. This is because of, e.g. incomplete knowledge of the material parameters, insufficient modelling accuracy or- especially in the case of optical microscopy-insufficient resolution. With decreasing CDs these systematic differences increase. The need on new cross-calibration strategies arises. Non-imaging metrology methods like scatterometry as non destructive, non diffraction limited, fast optical methods offer access to the geometrical parameters of periodic structures like e.g. top and bottom CD, pitch, side-wall angle, line height, or roughness. Therefore, these methods provide independently achieved additional information that can be used for cross-calibration. At the PTB two scatterometers are in use (VIS @ λ=633 nm and EUV @ λ=13.55 nm). A third device (DUV @ λ=193 nm) is under construction. It will offer a wide spectrum of measuring principles like scatterometry, ellipsometric scatterometry, reflectometry, polarisation reflectometry, and using a broadband light source spectroscopic ellipsometry and spectroscopic reflectometry. For simulation and modelling of the intensity distribution of the diffraction pattern two programs based on the rigorous coupled-wave analysis (RCWA) method and a finite element method (FEM), respectively are used. The program features will be illustrated. A comparison of the simulations with the results achieved with the scatterometers on different types of lithography masks (chrome on glass, EUV-masks) will be presented as well.

A new technology for the precise topography measurement of reflecting flat surfaces is presented in this paper. The instrument is capable of scanning large flats of about 500 mm/sup 2/. The instrument consists of a sensor head, which is an angle-measuring device, based on a CCD camera or a position sensitive detector (PSD). The sensor head includes a pentagon prism that reduces the pitch error in scan direction by a factor of about 100.

We present a novel deflectometric method for the ultra-precise 2D topography measurement of large optical surfaces. The approach is a 2D extension of the established Extended Shear Angle Difference (ESAD) technique, which has previously been limited to the 1D form measurement of plane or slightly curved surfaces. We report in detail on the new 2D ESAD scanning facility capable of measuring large (up to 600 mm in diameter) optical surfaces and present first measurement results. Information on the mathematical algorithms involved in the data acquisition and analysis are given and the mathematics used in the reconstruction of 2D topography maps from a set of angle difference data are described. The intricacies of 2D angle measurement with a modified autocollimator and calibration issues are discussed.

The technological limits to the beam quality of modern synchrotron‐radiation sources are set by the geometrical accuracy of the optical components. The fabrication of these components is limited by the measuring technique. The exactly measured topography of the surface under test (SUT) allows postprocessing (e.g. ion beam etching). For form components of the SUT this is possible between its whole length and some millimeters. Present measurement technologies such as long‐trace profilers, reach slope uncertainties down to 50 milli‐arcsec rms. Their height uncertainty corresponds to several tens of nanometers for a synchrotron mirror 1 m in length. The parabolic and long‐wave contributions of form in particular might differ due to systematic errors of the slope measurement. In the context of a cooperative research project initiated by BESSY, two profilers have been set up at the PTB — one for the absolute definition of flatness, the second presented here is faster and more robust. They operate with commercia...

The measurement of the topography or the nanotopography of large wafers up to 450 mm in diameter with satisfactory lateral resolution and nanometer uncertainty is still an unsolved problem. The topography of wafers covers a relatively large measurement range as wafers have surfaces with a so-called "slightly unflat" topography which mostly exceeds the measurement capabilities of interferometers. For the ultraprecise and traceable measurement of the slope and topography of slightly unflat optical surfaces, a novel scanning deflectometry principle has been developed. An uncertainty of the topography in the nanometer range will be achieved, as this principle minimizes error influences and allows a highly precise calibration of the angle measuring device. The main goal is to use this principle for the ultraprecise measurement of the nanotopography of large wafers. The measurement principle is based on the analysis of differences of reflection angles obtained at surface points which are separated by large lateral shears. It does not rely on external reference surfaces of matched topography and in first and second order is independent of any stage errors and the whole-body motion of the specimen. The measurands are directly traced back to the base units of angle and length. The specific idea of wafer measurement is to combine rotational and linear scanning with the measurement of slope difference vectors and to arrive at an unambiguous solution for the topography and nanotopography. The equations with the slope difference vectors are solved to reconstruct the slope vectors, as newly developed mathematical algorithms allow the surface slope to be reconstructed from slope differences for two different shears. This is reached by applying natural extensions and shearing transfer functions by a mathematically exact method over the whole surface area. Further the differential equations for the slope vectors are solved to unambiguously reconstruct the topography. With this method it is possible to achieve nanometer uncertainty and at the same time a high lateral resolution, short measurement times and the possibility of mastering the large measurement range necessary for slightly unflat wafer surfaces.

Ultrafast hole dynamics in Si0.5Ge0.5/Si multiple quantum wells is studied with resonant excitation of the HH1 ➙ HH2 heavy-hole intersubband transition. Pump-probe experiments with 150-fs mid-infrared pulses demonstrate intersubband scattering and thermalization on a subpicosecond timescale.

Summary form only given. Femtosecond pulses in the mid-infrared provide a broad potential for condensed matter studies enabling time-resolved investigations for instance of molecular vibrations or inter subband dynamics in semiconductor nanostructures. At wavelengths beyond 10 /spl mu/m, very short pulses of /spl ap/100-200-fs duration were obtained at high repetition rates by parametric mixing within the broad spectra of 13-fs pulses from a 2-MHz cavity-dumped Ti:sapphire oscillator in GaSe. From amplified systems, which intrinsically deliver much higher pulse energies, 130-fs pulses tunable from 3-10 /spl mu/m were generated by difference frequency mixing pulses from an optical parametric amplifier (OPA) in AgGaS/sub 2/, but for longer wavelengths the potential for generating such pulses shorter than 700 fs, has not yet been exploited. We demonstrate a kilohertz source of intense /spl ap/100-fs mid-infrared pulses with a tuning capability beyond 10 /spl mu/m. Near-infrared signal and idler pulses (/spl lambda/= 1-2 /spl mu/m) are generated in a two-pass, type II BBO OPA pumped by 200 /spl mu/J from a l-kHz, 800-nm Ti:sapphire regenerative amplifier.

Scatterometry is a common tool for the dimensional characterization of periodic nanostructures. It is an indirect measurement method, where the dimensions and geometry of the structures under test are reconstructed from the measured scatterograms applying inverse rigorous calculations. This approach is numerically very elaborate so that usually a number of approximations are used. The influence of each approximation has to be analysed to quantify its contribution to the uncertainty budget. This is a fundamental step to achieve traceability. In this paper, we experimentally investigate two common approximations: the effect of a finite illumination spot size and the application of a more advanced structure model for the reconstruction. We show that the illumination spot size affects the sensitivity to sample inhomogeneities but has no influence on the reconstruction parameters, whereas additional corner rounding of the trapezoidal grating profile significantly improves the reconstruction result.

A novel type of deep ultraviolet scatterometer recently developed and set up at PTB has been significantly improved with respect to the dynamic range and the signal-to-noise ratio of the measured scatterograms. The main modifications concern a novel digital data acquisition technique and a new method for the calibration of the applied detectors. With the improved system linewidths (critical dimensions), measurements on periodic structures on a state-of-the-art MoSi photomask have been carried out. The results are compared to those achieved with a scanning electron microscope and a spectroscopic scatterometer.