Hostname: page-component-8448b6f56d-42gr6 Total loading time: 0 Render date: 2024-04-23T11:24:56.229Z Has data issue: false hasContentIssue false

Sample Thickness Determination by Scanning Transmission Electron Microscopy at Low Electron Energies

Published online by Cambridge University Press:  13 December 2013

Tobias Volkenandt*
Laboratorium für Elektronenmikroskopie, Karlsruher Institut für Technologie (KIT), Engesserstr. 7, 76131 Karlsruhe, Germany
Erich Müller
Laboratorium für Elektronenmikroskopie, Karlsruher Institut für Technologie (KIT), Engesserstr. 7, 76131 Karlsruhe, Germany
Dagmar Gerthsen
Laboratorium für Elektronenmikroskopie, Karlsruher Institut für Technologie (KIT), Engesserstr. 7, 76131 Karlsruhe, Germany
*Corresponding author. E-mail:
Get access


Sample thickness is a decisive parameter for any quantification of image information and composition in transmission electron microscopy. In this context, we present a method to determine the local sample thickness by scanning transmission electron microscopy at primary energies below 30 keV. The image intensity is measured with respect to the intensity of the incident electron beam and can be directly compared with Monte Carlo simulations. Screened Rutherford and Mott scattering cross-sections are evaluated with respect to fitting experimental data with simulated image intensities as a function of the atomic number of the sample material and primary electron energy. The presented method is tested for sample materials covering a wide range of atomic numbers Z, that is, fluorenyl hexa-peri-hexabenzocoronene (Z = 3.5), carbon (Z = 6), silicon (Z = 14), gallium nitride (Z = 19), and tungsten (Z = 74). Investigations were conducted for two primary energies (15 and 30 keV) and a sample thickness range between 50 and 400 nm.

Techniques, Software, and Instrumentation Development
Copyright © Microscopy Society of America 2014 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)


Bishop, H. (1967). Electron scattering in thick targets. Br J Appl Phys 18, 703715.Google Scholar
Browning, R., Li, T., Chui, B., Ye, J., Pease, R., Czyzewski, Z. & Joy, D. (1994). Empirical forms for the electron/atom elastic scattering cross sections from 0.1 to 30 keV. J Appl Phys 76, 20162022.CrossRefGoogle Scholar
Czyzewski, Z., MacCallum, D., Romig, A. & Joy, D. (1990). Calculations of Mott scattering cross section. J Appl Phys 68, 30663072.CrossRefGoogle Scholar
Egerton, R. (1986). Electron Energy-Loss Spectroscopy in the Electron Microscope. New York: Plenum Press.Google Scholar
Gauvin, R. & Drouin, D. (1993). A formula to compute total elastic Mott cross-sections. Scanning 15, 140150.Google Scholar
Heinrich, K. (1981). Electron Beam X-Ray Microanalysis. New York: Van Nostrand Reinhold Company.Google Scholar
Joy, D. & Luo, S. (1989). An empirical stopping power relationship for low-energy electrons. Scanning 11, 176180.Google Scholar
Klein, T., Buhr, E. & Frase, C.G. (2012). TSEM: A review of scanning electron microscopy in transmission mode and its applications. In Advances in Imaging and Electron Physics, Hawkes, P.W. (Ed.), pp. 297356. New York: Elsevier.Google Scholar
Kotera, M., Murata, K. & Nagami, K. (1981). Monte Carlo simulation of 1–10 keV electron scattering in a gold target. J Appl Phys 52, 9971003.Google Scholar
Krzyzanek, V. & Reichelt, R. (2008). Mass thickness determination of thin specimens using high-resolution scanning electron microscopy. EMC 2008, 14th European Microscopy Congress, Aachen, September 1–5, 2008. Google Scholar
Lehmann, M. & Lichte, H. (2002). Tutorial on off-axis electron holography. Microsc Microanal 8, 447466.CrossRefGoogle ScholarPubMed
Morandi, V. & Merli, P. (2007). Contrast and resolution versus specimen thickness in low energy scanning transmission electron microscopy. J Appl Phys 101, 114917. Google Scholar
Mott, N.F. & Massey, H.S.W. (1949). The Theory of Atomic Collisions. Oxford, UK: Clarendon Press.Google Scholar
Motz, J., Olsen, H. & Koch, H. (1964). Electron scattering without atomic or nuclear excitation. Rev Mod Phys 36, 881928.Google Scholar
Murata, K., Matsukawa, T. & Shimizu, R. (1971). Monte Carlo calculations on electron scattering in a solid target. Jpn J Appl Phys 10, 678686.Google Scholar
Pfaff, M., Müller, E., Klein, M.F.G., Colsmann, A., Lemmer, U., Krzyzanek, V., Reichelt, R. & Gerthsen, D. (2011). Low-energy electron scattering in carbon-based materials analyzed by scanning transmission electron microscopy and its application to sample thickness determination. J Microsc 243, 3139.Google Scholar
Powell, C., Jablonski, A. & Salvat, F. (2005). NIST databases with electron elastic-scattering cross sections, inelastic mean free paths, and effective attenuation lengths. Surf Interface Anal 37, 10681071.Google Scholar
Reimer, L. (1998). Scanning Electron Microscopy. Heidelberg, Germany: Springer Verlag.Google Scholar
Reimer, L. & Lödding, B. (1984). Calculation and tabulation of Mott cross-sections for large-angle electron scattering. Scanning 6, 128151.Google Scholar
Ritchie, N. (2005). A new Monte Carlo application for complex sample geometries. Surf Interface Anal 37, 10061011.Google Scholar
Rosenauer, A., Gries, K., Müller, K., Pretorius, A., Schowalter, M., Avramescu, A., Engl, K. & Lutgen, S. (2009). Measurement of specimen thickness and composition in Al x Ga1−x N/GaN using high-angle annular dark field images. Ultramicroscopy 109, 11711182.CrossRefGoogle Scholar
Rutherford, E. (1911). The scattering of α- and β-particles by matter and the structure of the atom. Phil Mag 21, 669688.CrossRefGoogle Scholar
Salvat, F., Jablonski, A. & Powell, C.J. (2005). ELSEPA—Dirac partial-wave calculation of elastic scattering of electrons and positrons by atoms, positive ions and molecules. Comput Phys Commun 165, 157190.Google Scholar
Scholze, F., Henneken, H., Kuschnerus, P., Rabus, H., Richter, M. & Ulm, G. (2000). Determination of the electron-hole pair creation energy for semiconductors from the spectral responsivity of photodiodes. Nucl Instrum Meth A 439, 208215.Google Scholar
Shimizu, R. & Ding, Z.-J. (1992). Monte Carlo modeling of electron-solid interactions. Rep Prog Phys 55, 487531.Google Scholar
Treacy, M. & Gibson, J. (1993). Coherence and multiple scattering in “Z-contrast” images. Ultramicroscopy 52, 3153.Google Scholar
Van den Broek, W., Rosenauer, A., Goris, B., Martinez, G., Bals, S., Van Aert, S. & Van Dyck, D. (2012). Correction of non-linear thickness effects in HAADF STEM electron tomography. Ultramicroscopy 116, 812.Google Scholar
Volkenandt, T., Müller, E., Hu, D., Schaadt, D. & Gerthsen, D. (2010). Quantification of sample thickness and In-concentration of InGaAs quantum wells by transmission measurements in a scanning electron microscope. Microsc Microanal 16, 604613.Google Scholar
Williams, D.B. & Carter, C.B. (2009). Transmission Electron Microscopy. New York: Springer.CrossRefGoogle Scholar