| Zugriffsnummer | 27390 |
| Dokumenttyp | Konferenzartikel |
| Sprache | Englisch |
| Titel | Stochastic modelling aspects for an improved solution of the inverse problem in scatterometry |
| Autor(in); Institution |
Gross, Hermann; 8.4, Mathematische Modellierung und Datenanalyse, PTB-Berlin
Henn, Mark-Alexander; 8.4, Mathematische Modellierung und Datenanalyse, PTB-Berlin
Rathsfeld, A.; Weierstrass Institute of Applied Analysis and Stochastics, Berlin, GERMANY
Bär, Markus; 8.4, Mathematische Modellierung und Datenanalyse, PTB-Berlin
|
| Quelle/Jahr | Advanced mathematical and computational tools in metrology and testing : AMCTM IX:(2012), 202 - 209 |
| Schriftenreihe | Series on Advances in Mathematics for Applied Sciences: 84 |
| Herausgeber(in) |
Pavese, F.; Istituto Nazinale di Ricerca Metrologica, Torino, ITALY
Bär, Markus; 8.4, Mathematische Modellierung und Datenanalyse, PTB-Berlin
Filtz, J-R.; Laboratoire National de Métrologie et d'Essais, Paris, FRANCE
Forbes, Alistair; National Physical Laboratory, Teddington, Middlesesx, UNITED KINGDOM
Pendrill, L.; SP Technical Research Institute of Sweden, Boras, SWEDEN
Shirono, K.; National Metrology Institute of Japan, AIST, Tsukuba, JAPAN
|
| ISSN | 1793-0901 |
| ISBN | 978-981-4397-94-0 ; 981-4397-94-6 |
| Verlag | Singapore [u.a.]: World Scientific Publ. |
| Konferenzangaben | Advanced mathematical and computational tools in metrology and testing: AMCTM IX, Göteborg, 20-22, June, 2011, Sweden |
| Freie Schlagworte | scatterometry ; line roughness ; LER ; LWR ; uncertainties |
| Zusammenfassung | In wafer metrology scatterometry is an established method to determine the critical dimensions (CD) of periodic surface structures from the measured light diffraction pattern. These CDs include line widths, heights and side-wall angles in the sub-micrometer range. In extreme ultraviolet (EUV) scatterometry the incident light has wavelengths in a small range around 13.5 nm and the measured light diffraction pattern consists of many plane wave modes, the so-called orders. The intensity distribution over these modes characterizes the profile geometry and the optical properties of the illuminated surface structure. The rigorous numerical simulation of the diffraction process for periodic 2D structures can be realized by the finite element solution (FEM) of the two-dimensional Helmholtz equation. The inverse problem is formulated as a non-linear operator equation and can be solved by iterative methods, i.e., by an iterative variation of the model parameters to minimize the deviation of the measured efficiency or phase shift values from the calculated ones. Clearly, the uncertainties of the reconstructed geometric parameters depend on the uncertainties of the input data and can be estimated by various methods like Monte Carlo or approximative covariance methods. Furthermore, aperiodic perturbations in the examined line structures affect the uncertainties. In order to clear the impact of line edge and line width roughness, we present an FEM based method to simulate diffraction patterns for structures with aperiodic random perturbations. We apply this for a typical EUV mask composed of TaN-absorber lines of about 80 nm height and 93.33 nm width, a period of 280 nm, and with an underlying MoSi-multilayer stack of 360 nm thickness. A systematic decrease of the mean efficiencies for higher diffraction orders along with increasing variances is observed and established for different degrees of roughness. As a consequence this systematic bias has to be included in the reconstruction model to provide accurate values for the reconstructed profile parameters. |
Zitierung
Gross, H., Henn, M.-A., Rathsfeld, A., & Bär, M. (2012). Stochastic modelling aspects for an improved solution of the inverse problem in scatterometry. Advanced mathematical and computational tools in metrology and testing: AMCTM IX, Göteborg, 20-22, June, 2011, Sweden.