# High Resolution Metrology and Simulation

The goal of our group “High-resolution measurement and simulation” is the investigation and development of optical measurement techniques that allow high-precision measurements in the subwavelength domain. In particular, our work focuses on the characterization of optical surfaces and volumes as well as technical surfaces in the field of semiconductor industry.

Today's accuracy requirements of optical metrology are two orders of magnitude beyond the diffraction limit. Hence, a precise understanding of the interaction of light with the studied structure is essential. The need to resolve structural details in the traditional sense may be increasingly replaced by a highly accurate model-based object reconstruction.

Our emphasis lies on the rigorous simulation of the actual light-structure interaction including the modeling of complete optical measurement processes. On the other hand, we experimentally investigate new and proven methods for metrology that use besides the intensity also the polarization and phase of the light as additional information channels to obtain maximum structural information accuracy. Our measurement methods include various microscopic methods as well as diffraction and polarization-resolved scatterometry.

In addition to structural dimensions of individual selected structures also the determination of existing defects on the wafer is necessary for process control in semiconductor industry. From knowledge of the defect density, defect types and their distribution, action can be taken to increase yield of a specific process. For such measurement tasks the method of scatterometry is inappropriate because it’s too slow for measuring representative sets of structures on an entire wafer.

With the help of defectoscopy, however, one can quickly investigate a large number of structures simultaneously. For this purpose a microscopic setup is used, which cannot provide a fully resolved image of these structures anymore. An advantageous feature of defects compared to structures is, that in practice defects occur in isolation, which means that in a periodic array of identical structures significantly different optical properties are present in isolated areas. Under certain lighting conditions, these objects appear as bright or dark pixels in the microscopic image, regardless of how large the structures or defects are. These lighting conditions can then be used as a specific signature to distinguish between different defects. These signatures can be developed together with the introduction of a new process using rigorous simulations.

### Publications

- S. Rafler; T. Schuster; K. Frenner; W. Osten; U. Seifert: Improvements on the simulation of microscopic images for the defect detection of nanostructures, Proc. SPIE 6922 (2008) 692215
- S. Rafler; M. Petschow; U. Seifert; K. Frenner; W. Osten: Effects of Pupil Discretization and Littrow illumination in the Simulation of Bright-field defect detection, Optics Letters 34, Issue 12, p. 1840 (2009)

The theory of diffraction according to Fresnel or Kirchoff is a scalar wave theory which is not sufficient to describe various optical effects. This is so because physical boundary conditions have to be neglected with a scalar approach. Real electromagnetic corrugations are vectorial waves. As structure sizes decreases particularly in semiconductor technology, patterns with dimensions comparable to the wavelenght of visible light become focus of research. There, interaction effects of light and structure strongly influence diffraction spectra of reflected and trasmitted light. These contributions can be merely considered by rigorous calculations applying full vectorial Maxwell equations. In contrast to scalar optics there are only few analytical solutions for rigorous diffraction so numerical methods are used inpractice. ITO has been active in the field of rigorous numerical simulation of diffraction on periodic structures since end of 1990. Since then, our simulation tool Microsim, which is powered by a rigorous coupled wave approximation (RCWA), has been continuously used and improved.

You can find more details about Microsim in our software section..

### Veröffentlichungen

- M. Totzeck, "Numerical simulation of high-NA quantitative polarization microscopy and corresponding near-fields", Optik, 112 (2001) 381-390
- Reinig P., Dost R., Mört M., Hingst, T., Mantz U., Schuster, T. Kerwien, N., Kaufmann J., Osten W.: "Potential and limits of scatterometry: A study on bowed profiles and high aspect ratios", Scatterometry Workshop 2004, 3.-5.5.2004 Porquerolles, Frankreich
- R. Berger, J. Kauffmann, N. Kerwien, W. Osten, H.J. Tiziani: Rigorose Beugungssimulation: Ein Vergleich zwischen RCWA, DTD und der Finiten Elemente Methode, 105. DgaO-Tagung 2004 P59
- Kerwien N., Schuster T., Rafler S., Osten W., "Semi-rigorous Diffraction Theory: Realization of Classical Concepts in the Framework of Electrodynamics", J. Opt. Soc. Am. A 24 (2007) No. 4 1074-1084

The term scatterometry summarizes multiple non-imaging optical measurement methods used to reconstruct periodic structures down to nanometer size, i.e. below the optical Abbe-limit. Scatterometry has proved to be a powerful technique for CD and profile metrology and has established itself as one of the mainly applied methods for CD metrology in semiconductor industry.

## Finished Projects:

- Design and Fabrication of Near- to Far-Field Transformers by Sub-100 nm Two-Photon-Polymerization (DFG)
- Development of functional sub-100 nm structures with 3D-Two-Photon-Polymerisation-Technique and optical methods for characterization (DFG)

## Publications:

- Ferreras Paz, V., Frenner, K., & Osten, W. (2014). Increasing Scatterometric Sensitivity by Simulation Based Optimization of Structure Design. In W. Osten (Ed.), Fringe 2013 - 7th International Workshop on Advanced Optical Imaging and Metrology (pp. 345–348). Springer Berlin Heidelberg.
- Ferreras Paz, V., Peterhänsel, S., Frenner, K., & Osten, W. (2012). Solving the inverse grating problem by white light interference Fourier scatterometry. Nature Light: Science & Applications, 1(11), e36.
- Bilski, B., Frenner, K., & Osten, W. (2011). About the influence of Line Edge Roughness on measured effective–CD. Optics Express, 19(21), 19967.
- Ferreras Paz, V., Peterhänsel, S., Frenner, K., Osten, W., Ovsianikov, A., Obata, K., & Chichkov, B. (2011). Depth sensitive Fourier-Scatterometry for the characterization of sub-100 nm periodic structures. In Proceedings of SPIE (Vol. 8083, p. 80830M–80830M–9).
- Osten, W., Ferreras Paz, V., Frenner, K., Schuster, T., & Bloess, H. (2009). Simulations of Scatterometry Down to 22 nm Structure Sizes and Beyond with Special Emphasis on LER. In AIP Conference Proceedings (Vol. 1173, pp. 371–378). AIP.
- Schuster, T., Rafler, S., Ferreras Paz, V., Frenner, K., & Osten, W. (2009). Fieldstitching with Kirchhoff-boundaries as a model based description for line edge roughness (LER) in scatterometry. Microelectronic Engineering, 86(4-6), 1029–1032.
- T. Schuster, S. Rafler, W. Osten, P. Reinig, T. Hingst, "Scatterometry from crossed grating structures in different configurations", Proc. SPIE 6617, 661715-1 – 661715-9 (2007)
- M. Totzeck: „Numerical simulation of high-NA quantitative polarization microscopy and corresponding near-fields", Optik 112 (9), 399-406 (2001)

Objects in nature consist of atoms and molecules that are arranged in specific patterns dictated by the laws of physics and chemistry. Those patterns determine the electromagnetic properties of the material in question, and in turn how they influence electromagnetic waves. By designing arrangements of shapes with features that are smaller than a given wavelength, so called metamaterials can be developed in such a way that they have properties, which do not exist in nature. At ITO we focus our investigations on so called super lenses, which have unprecedented imaging and magnification abilities.

The key to understanding the underlying physical principles of the imaging properties of metamaterial structures is the simulation of resonant interactions between excited surface waves (surface plasmon polaritons) and the electromagnetic field. Particularly suitable are rigorous methods like the RCWA (Rigorous Coupled Wave Algorithm) which is utilized in Microsim, a software that was developed at our institute. Due to the complex calculation algorithms, convergence enhancements play a major role in terms of computation time reduction (especially for structures comprised of metal). Furthermore, we're operating a Helios NanoLab DualBeam of FEI, which allows us to manufacture the designed nanostructures ourselves.

Current project: DFG Superlinse

### Publications:

- S. Maisch, P. Schau, K. Frenner, W. Osten, "About the feasibility of nearfield-farfield transformers based on optical metamaterials" in Fringe 2009: 6th International Workshop on Advanced Optical Metrology (2009), 375–383.
- P. Schau, K. Frenner, L. Fu, H. Schweizer, W. Osten, "Coupling between surface plasmons and Fabry-Pérot modes in metallic double meander structures" in Proc. SPIE 7711 (2010), 77111F
- L. Fu, H. Schweizer, T. Weiss, P. Schau, K. Frenner, W. Osten, H. Giessen, D. N. Chigrin, "Mode hybridization and interaction in a metallic meander Fabry-Pérot cavity" in AIP Conf. Proc. 1291 (2010), Vol. 1291, 115–117.
- P. Schau, K. Frenner, L. Fu, H. Schweizer, H. Giessen, W. Osten, "Rigorous modeling of meander-type metamaterials for sub-lambda imaging" in Proc. SPIE 8083 (2011), 808303
- H. Schweizer, L. Fu, N. Liu, T. Weiss, P. Schau, K. Frenner, W. Osten, H. Giessen, "The promise of metamaterials for new applications in optics" in Proc. SPIE 8083 (2011), 808302
- P. Schau, K. Frenner, L. Fu, W. Osten, H. Schweizer, H. Giessen, "Sub-wavelength imaging using stacks of metallic meander structures with different periodicities" in Proc. SPIE 8093 (2011), 80931K
- L. Fu, P. Schau, K. Frenner, W. Osten, T. Weiss, H. Schweizer, H. Giessen, "Mode coupling and interaction in a plasmonic microcavity with resonant mirrors", Phys. Rev. B 84, 1–6 (2011)
- L. M. Gaspar Venancio, S. Hannemann, G. Lubkowski, M. Suhrke, H. Schweizer, L. Fu, H. Giessen, P. Schau, K. Frenner, W. Osten, "Metamaterials for optical and photonic applications for space: preliminary results" in Proc. SPIE 8146, (2011), 81460E
- P. Schau, K. Frenner, L. Fu, H. Schweizer, H. Giessen, W. Osten, "Design of high-transmission metallic meander stacks with different grating periodicities for subwavelength-imaging applications", Opt. Express 19, 3627–3636 (2011)
- P. Schau, L. Fu, K. Frenner, M. Schäferling, H. Schweizer, H. Giessen, L. M. G. Venancio, W. Osten, "Polarization scramblers with plasmonic meander-type metamaterials", Opt. Express 20, 22700 (2012)
- P. Schau, L. Fu, K. Frenner, H. Schweizer, M. Schäferling, T. Weiss, H. Giessen, L. M. Gaspar Venancio, S. Hannemann, W. Osten, "Polarization scrambling with metallic meander structures for space applications" in Proc. SPIE 8423, (2012), 842314
- L. Fu, P. Schau, K. Frenner, H. Schweizer, J. Zhao, B. Frank, L. Wollet, P. Gaiser, B. Gompf, H. Giessen, W. Osten, "Experimental demonstration of dispersion engineering through mode interactions in plasmonic microcavities" in Proc. SPIE 8423 (2012), p. 84232I
- H. Schweizer, L. Fu, M. Hentschel, T. Weiss, C. Bauer, P. Schau, K. Frenner, W. Osten, H. Giessen, "Resonant multimeander-metasurfaces: A model system for superlenses and communication devices", Phys. status solidi 249, 1415–1421 (2012)

### Projects

- DFG Superlens
- Speckle Simulation
- FluoTis

### Completed Projects

- Optical Metamaterials for Metrology Applications (OPTIM)
- Metamaterials for Optical and Photonic Applications in Space
- Design and Fabrication of Near- to Far-Field Transformers by Sub-100 nm Two-Photon-Polymerization (DFG)
- Development of functional sub-100 nm structures with 3D-Two-Photon-Polymerisation-Technique and optical methods for characterization (DFG)