Correction of non-linear thickness effects in HAADF STEM electron tomography

Abstract In materials science, high angle annular dark field scanning transmission electron microscopy is often used for tomography at the nanometer scale. In this work, it is shown that a thickness dependent, non-linear damping of the recorded intensities occurs. This results in an underestimated intensity in the interior of reconstructions of homogeneous particles, which is known as the cupping artifact. In this paper, this non-linear effect is demonstrated in experimental images taken under common conditions and is reproduced with a numerical simulation. Furthermore, an analytical derivation shows that these non-linearities can be inverted if the imaging is done quantitatively, thus preventing cupping in the reconstruction.

[1]  G. Möbus,et al.  Reconstruction of 3D morphology of polyhedral nanoparticles , 2007 .

[2]  H. Rose,et al.  Conditions and reasons for incoherent imaging in STEM , 1996 .

[3]  S. Pikker,et al.  Springer Proceedings in Physics , 2013 .

[4]  D. Muller,et al.  Three-dimensional imaging of nanovoids in copper interconnects using incoherent bright field tomography , 2006 .

[5]  K. S. Kölbig,et al.  Errata: Milton Abramowitz and Irene A. Stegun, editors, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, National Bureau of Standards, Applied Mathematics Series, No. 55, U.S. Government Printing Office, Washington, D.C., 1994, and all known reprints , 1972 .

[6]  Avinash C. Kak,et al.  Principles of computerized tomographic imaging , 2001, Classics in applied mathematics.

[7]  Susanne Stemmer,et al.  Experimental quantification of annular dark-field images in scanning transmission electron microscopy. , 2008, Ultramicroscopy.

[8]  Milton Abramowitz,et al.  Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables , 1964 .

[9]  Joachim Frank,et al.  Electron Tomography , 1992, Springer US.

[10]  Zachary H. Levine,et al.  Theory of bright-field scanning transmission electron microscopy for tomography , 2005 .

[11]  Russell F. Loane,et al.  Annular dark-field imaging: Resolution and thickness effects , 1993 .

[12]  R. Leapman,et al.  Monte Carlo electron-trajectory simulations in bright-field and dark-field STEM: implications for tomography of thick biological sections. , 2009, Ultramicroscopy.

[13]  L. Reimer Transmission Electron Microscopy: Physics of Image Formation and Microanalysis , 1989 .

[14]  Peter Hawkes,et al.  The Electron Microscope as a Structure Projector , 2007 .

[15]  David B. Williams,et al.  Transmission Electron Microscopy: A Textbook for Materials Science , 1996 .

[16]  Adrian Avramescu,et al.  Measurement of specimen thickness and composition in Al(x)Ga(1-x)N/GaN using high-angle annular dark field images. , 2009, Ultramicroscopy.

[17]  Z. Saghi,et al.  Electron tomography of regularly shaped nanostructures under non‐linear image acquisition , 2008, Journal of microscopy.

[18]  Susanne Stemmer,et al.  Quantitative atomic resolution scanning transmission electron microscopy. , 2008, Physical review letters.

[19]  Gao,et al.  Parameterization of the temperature dependence of the Debye-Waller factors. , 1999, Acta crystallographica. Section A, Foundations of crystallography.

[20]  Z. Levine Tomography in the multiple scattering regime of the scanning transmission electron microscope , 2003 .