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Measurements of lithographic masks based on scatterometry

 ptblogo

Duration

November 2008 - October 2010

Project leader

A. Rathsfeld

Assistant

T. Arnold

Cooperation

Physikalisch-Technische Bundesanstalt


Support

Subcontract of BMBF project CDur32

Introduction

The production of computer chips with increasingly small details requires more and more accurate measurement techniques. In particular, the development and evaluation of photolithographic manufacturing methods necessitate a high precision measurement of special test geometries, which can be generated on the surface of lithographic masks and wafers. Besides well-established measurement techniques including atomic force microscopy (AFM) and scanning electron microscopy (SEM), the fast and non-destructive scatterometric methods are promising. In contrast to the optical microscopy, scatterometry does not produce a true image of the target. Instead, a scattered far-field pattern is measured, from which the geometry data is extracted by using a mathematical algorithm and a model assumption for the geometry. In other words, an inverse problem for the reconstruction of the geometry data is to be solved.

Goals of Project

  • Simulation of diffraction: 2D and 3D solver for time-harmonic Maxwell's equations over biperiodic cells
  • Derivatives of diffraction efficiencies with respect to geometry parameters
  • Inverse problem: Optimization of least square functional of deviation from measured efficiencies (far-field pattern)
  • Evaluate the affect of systematic model errors and stochastic uncertainties on the reconstruction accuracy

Publications

  • H. GROSS, A. RATHSFELD, F. SCHOLZE, M. BÄR, Profile reconstruction in extreme ultraviolet (EUV) scatterometry: Modeling and uncertainty estimates, Meas. Sci. Technol., 20 (2009) pp. 105102/1--105102/11.
  • H. GROSS, A. RATHSFELD, M. BÄR, Modelling and uncertainty estimates for numerically reconstructed profiles in scatterometry, in: Advances Mathematical & Computational Tools in Metrology & Testing VIII, F. PAVESE, M. BÄR, A.B. FORBES, J.M. LINARES, C. PERRUCHET, N.F. ZHANG, eds., vol. 78 of Series on Advances in Mathematics for Applied Sciences, World Scientific, Singapore, 2009, pp. 142--147.
  • H. GROSS, F. SCHOLZE, A. RATHSFELD, M. BÄR, Evaluation of measurement uncertainties in EUV scatterometry, in: Modeling Aspects in Optical Metrology II, H. BOSSE, B. BODERMANN, R.M. SILVER, eds., vol. 7390 of Proceedings of SPIE, SPIE, 2009, pp. 7390OT/1--7390OT/11.
  • H. GROSS, F. SCHOLZE, A. RATHSFELD, M. BÄR, Evaluation of measurement uncertainties in EUV scatterometry, in: Modeling Aspects in Optical Metrology II, H. BOSSE, B. BODERMANN, R.M. SILVER, eds., vol. 7390 of Proceedings of SPIE, SPIE, 2009, pp. 7390OT/1--7390OT/11.
  • M.-A. HENN, R. MODEL, M. BÄR, M. WURM, B. BODERMANN, A. RATHSFELD, H. GROSS, On numerical reconstructions of lithographic masks in DUV scatterometry, in: Modeling Aspects in Optical Metrology II, H. BOSSE, B. BODERMANN, R.M. SILVER, eds., vol. 7390 of Proceedings of SPIE, SPIE, 2009, pp. 7390OQ/1--7390OQ/11.
  • H. GROSS, R. MODEL, A. RATHSFELD, F. SCHOLZE, M. WURM, B. BODERMANN, M. BÄR, Modellbildung, Bestimmung der Messunsicherheit und Validierung für diskrete inverse Probleme am Beispiel der Scatterometrie, in: Sensoren und Messsysteme, 14. Fachtagung Ludwigsburg, 11./12. März 2008, vol. 2011 of VDI-Berichte, VDI, 2008, pp. 337--346.
  • R. MODEL, A. RATHSFELD, H. GROSS, M. WURM, B. BODERMANN, A scatterometry inverse problem in optical mask metrology, in: 6th International Conference on Inverse Problems in Engineering: Theory and Practice, 15--19 June 2008, Dourdan (Paris), France, vol. 135 of J. Phys.: Conf. Ser., Inst. Phys., 2008, pp. 012071/1--012071/8.
  • H. GROSS, A. RATHSFELD, Sensitivity analysis for indirect measurement in scatterometry and the reconstruction of periodic grating structures, Waves Random Complex Media, 18 (2008) pp. 129--149.
  • M. WURM, B. BODERMANN, F. SCHOLZE, CH. LAUBIS, H. GROSS, A. RATHSFELD, Untersuchung zur Eignung der EUV-Scatterometrie zur quantitativen Charakterisierung periodischer Strukturen auf Photolithographiemasken, in: Proc. of the 107th Meeting of DGaO (German Branch of the European Optical Society), June 6--10, 2006, in Weingarten, DGaO-Proceedings, 2006, pp. P74/1--P74/2.
  • H. GROSS, R. MODEL, M. BÄR, M. WURM, B. BODERMANN, A. RATHSFELD, Mathematical modelling of indirect measurements in scatterometry, Measurement, 39 (2006) pp. 782--794.

created: Febr. 26, 2010 by rathsfeld@wias-berlin.de
last modified: Mar. 10, 2010 by arnold@wias-berlin.de
URL: http://www.wias-berlin.de/contact/staff/index.jsp?lang=1&uname=arnold