Karsten Frenner

Normal vector method for the RCWA with automated vector field generation

Early formulations of the RCWA yield, implicated by the erroneous application of factorization rules to discrete Fourier transformations, poor convergence in certain cases. An explanation for this finding and an approach to overcome the problem for crossed gratings was first given by Li [J. Opt. Soc. Am. A 13, 1870 (1996) and 14, 2758 (1997)]. A further improvement was achieved by Schuster et al. [J. Opt. Soc. Am. A 24, 2880 (2007)], using a structure dependent normal vector (NV) field. While it is trivial to create those NV fields for simple geometrical shapes, to our knowledge an appropriate algorithm for arbitrary shapes does not exist, yet. In this work we present such an algorithm.

Development of functional sub-100 nm structures with 3D two-photon polymerization technique and optical methods for characterization

Investigations of two-photon polymerization (TPP) with sub-100 nm in the structuring resolution are presented by using photosensitive sol-gel material. The high photosensitivity of this material allows for TPP using a large variety in laser pulse durations covering a range between sub-10 fs and ≈140 fs. In this study, the authors demonstrate TPP structuring to obtain sub-100 nm in resolution by different approaches, namely, by adding a cross-linker to the material and polymerization with sub-10 fs short pulses. Additionally, a simulation and model based characterization method for periodic sub-100 nm structures was implemented and applied in an experimental white light interference Fourier-Scatterometry setup.

Design of high-transmission metallic meander stacks with different grating periodicities for subwavelength-imaging applications

When replacing a bulk negative index material (NIM) with two resonant surfaces that allow for surface plasmon polariton (SPP) propagation it is possible to recreate the same near-field imaging effects as with Pendrys perfect lens. We show that a metallic meander structure is perfectly suited as such a resonant surface due to the tunability of the short (SRSPP) and long range surface plasmon (LRSPP) frequencies by means of geometrical variation. Furthermore, the Fano-type pass band between the SRSPP and LRSPP frequencies of a single meander sheet retains its dominant role when being stacked. Hence, the pass band frequency position, which is determined by the meander geometry, controls also the pass band of a meander stack. When building up stacks with different periodicities the pass band shifts in frequency for each sheet in a different way. We rigorously calculate the spectra of various meander designs and show that this shift can be compensated by changing the remaining geometrical parameters of each single sheet. We also present a basic idea how high- transmission stacks with different periodicities can be created to enable energy transfer at low loss over practically arbitrary distances inside such a stack. The possibility to stack meander sheets of varying periodicity might be the key to far field superlenses since a controlled transformation of evanescent modes to traveling wave modes of higher diffraction order could be enabled.

Investigation of methods to set up the normal vector field for the differential method

In Fourier modal methods like the RCWA and the Differential Method the Li-rules for products in truncated Fourier space have to be obeyed in order to achieve good convergence of the results with respect to the mode number. The Lirules have to be applied differently for parts of the field that are tangential and orthogonal to material boundaries. This is achieved in the Differential Method by including a field of vectors in the calculation that are normal to the material boundaries. The same can be done laterally in each layer of an RCWA calculation of a 2-D periodic structure. It turns out that discontinuities in the normal vector field can disturb the computation especially when metallic materials are dominant in the structure which would make the usefulness of the normal vector method questionable. So it is of great importance to investigate how normal vector fields can be established with as few discontinuities as possible. We present various methods for the 2-D RCWA and the 1-D and 2-D Differential Method and compare the respective convergence behaviors. Especially we emphasize methods that are automatic and require as few user input as possible.

About the influence of Line Edge Roughness on measured effective-CD.

Various reports state that Line Edge/Width Roughness (LER/LWR) has a significant impact on the integrated circuits fabricated by means of lithography, hence there is a need to determine the LER in-line so that it never exceeds certain specified limits. In our work we deal with the challenge of measuring LER on 50 nm resist gratings using scatterometry. We show by simulation that there is a difference between LER and no-LER scatter signatures which first: depends on the polarization and second: is proportional to the amount of LER. Moreover, we show that the mentioned difference is very specific, that is - a grating with LER acts like a grating without LER but showing another width (CD, Critical Dimension), which we refer-to as effective-CD.

Influence of line edge roughness (LER) on angular resolved and on spectroscopic scatterometry

Scatterometry or optical CD metrology (OCD) has become one of the most common techniques in quantitative wafer metrology within the recent years. Different tool configurations are either available in commercial inspection tools or subject of recent and present research activities. Among these are normal incidence reflectometry, 2-θ scatterometry, spectroscopic ellipsometry and angle resolved Fourier scatterometry. The two latter techniques appear to be promising for future use in semiconductor fabs. Spectroscopic ellipsometry is well established, and Fourier scatterometry has become of increasing interest within the recent time. Line edge roughness, i.e. an edge position variation of printed lines in lithography, has been of less importance up to now, as its amplitude could largely be neglected with respect to the feature dimensions. This will, however, not be the case for future nodes, as on the one hand CDs are getting smaller and smaller, and on the other hand, even the absolute amplitude is expected to increase due to the higher complexity of lithography and etch processes. In this paper a comparison of scatterometric reconstructions in both spectroscopic and angle resolved techniques considering LER afflicted samples is presented. The validity and benefit of a simple effective medium model is investigated.

Polarization scramblers with plasmonic meander-type metamaterials

Due to plasmonic excitations, metallic meander structures exhibit an extraordinarily high transmission within a well-defined pass band. Within this frequency range, they behave like almost ideal linear polarizers, can induce large phase retardation between s- and p-polarized light and show a high polarization conversion efficiency. Due to these properties, meander structures can interact very effectively with polarized light. In this report, we suggest a novel polarization scrambler design using spatially distributed metallic meander structures with random angular orientations. The whole device has an optical response averaged over all pixel orientations within the incident beam diameter. We characterize the depolarizing properties of the suggested polarization scrambler with the Mueller matrix and investigate both single layer and stacked meander structures at different frequencies. The presented polarization scrambler can be flexibly designed to work at any wavelength in the visible range with a bandwidth of up to 100 THz. With our preliminary design, we achieve depolarization rates larger than 50% for arbitrarily polarized monochromatic and narrow-band light. Circularly polarized light could be depolarized by up to 95% at 600 THz.

Simulations of Scatterometry Down to 22 nm Structure Sizes and Beyond with Special Emphasis on LER

In recent years, scatterometry has become one of the most commonly used methods for CD metrology. With decreasing structure size for future technology nodes, the search for optimized scatterometry measurement configurations gets more important to exploit maximum sensitivity. As widespread industrial scatterometry tools mainly still use a pre‐set measurement configuration, there are still free parameters to improve sensitivity. Our current work uses a simulation based approach to predict and optimize sensitivity of future technology nodes. Since line edge roughness is getting important for such small structures, these imperfections of the periodic continuation cannot be neglected. Using fourier methods like e.g. rigorous coupled wave approach (RCWA) for diffraction calculus, nonperiodic features are hard to reach. We show that in this field certain types of fieldstitching methods show nice numerical behaviour and lead to useful results.

Phase-sensitive structured illumination to detect nanosized asymmetries in silicon trenches

Abstract. A metrology approach to detect nanoscale asymmetries in structures on a silicon wafer is being introduced through simulation investigations. The simulations were performed based on a rigorous coupled-wave analysis. A structured spot focused on the wafer with a high-numerical aperture (NA=0.7) has been scanned over the wafer. Having access to the complex amplitude of the wavefront over the field, both the intensity and the phase profile of the spot have been investigated in the far-field image plane. To show the proof of concept, we considered a 10-nm asymmetry that appears in the radius of the bottom roundings of a trench on the wafer. The results have been compared to the case of using a conventional spot and it has been shown that the structured illumination provides more sensitivity to the presence of asymmetry. In both illumination cases, the phase distribution along the spot was shown to be more sensitive to the changes due to the presence of asymmetry in the wafer.

Coupling between surface plasmons and Fabry-Pérot modes in metallic double meander structures

The excitation and transfer of evanescent electromagnetic waves appears as key challenge for the realization of optical imaging devices with super resolution. In this process surface plasmon polaritons (SPP) overtake the role as indispensable mediators between source fields and propagating fields. Therefore, the interaction between SPPs and the vacuum field in a double meander structure (DMS) is investigated. The occurrence of Fabry-Pérot (FP) modes within such a cavity and the SPP modes of the meander structure is analyzed to understand the interaction of both mode systems in the combined double meander structure. We show that the known Fano-type passband of single meander structures keeps its dominant role in the DMS and demonstrate the frequency selective role of meander mirrors within this meander cavity. The meander geometry determined passband frequency position also controls nearly solely the passband of the DMS. For far field superlenses (FSL) the energy transfer at low loss over practically arbitrary distances inside the structure is a key property. A resonant amplitude transfer can be obtained between resonantly coupled meander surfaces for unlimited distances in practical cases. This property enables a controlled transformation of evanescent modes to traveling wave modes of higher diffraction order useful for superlens operation.