Skip to main content

Strain Measurement in Semiconductor Heterostructures by Scanning Transmission Electron Microscopy

  • Knut Müller (a1), Andreas Rosenauer (a1), Marco Schowalter (a1), Josef Zweck (a2), Rafael Fritz (a2) and Kerstin Volz (a3)...

This article deals with the measurement of strain in semiconductor heterostructures from convergent beam electron diffraction patterns. In particular, three different algorithms in the field of (circular) pattern recognition are presented that are able to detect diffracted disc positions accurately, from which the strain in growth direction is calculated. Although the three approaches are very different as one is based on edge detection, one on rotational averages, and one on cross correlation with masks, it is found that identical strain profiles result for an In x Ga1−x N y As1−y /GaAs heterostructure consisting of five compressively and tensile strained layers. We achieve a precision of strain measurements of 7–9·10−4 and a spatial resolution of 0.5–0.7 nm over the whole width of the layer stack which was 350 nm. Being already very applicable to strain measurements in contemporary nanostructures, we additionally suggest future hardware and software designs optimized for fast and direct acquisition of strain distributions, motivated by the present studies.

Corresponding author
* * Corresponding authors. E-mail:;
Hide All

A. Rosenauer and K. Müller contributed to the present work in equal part and share first-authorship.

Hide All
Armigliato, A., Frabboni, S. & Gazzadi, G.C. (2008). Electron diffraction with ten nanometer beam size for strain analysis of nanodevices. Appl Phys Lett 93(16), 161906.
Bayle, P., Deutsch, T., Gilles, B., Lançon, F., Marty, A. & Thibault, J. (1994). Quantitative analysis of the deformation and chemical profiles of strained multilayers. Ultramicroscopy 56(1-3), 94107.
Béché, A., Rouvière, J.L., Clément, L. & Hartmann, J.M. (2009). Improved precision in strain measurement using nanobeam electron diffraction. Appl Phys Lett 95(12), 123114.
Bierwolf, R., Hohenstein, M., Phillipp, F., Brandt, O., Crook, G. & Ploog, K. (1993). Direct measurement of local lattice distortions in strained layer structures by HREM. Ultramicroscopy 49(1-4), 273285.
Bragg, W.H. & Bragg, W.L. (1913). The reflection of X-rays by crystals. Proc Roy Soc Lond A 88, 428438.
Chapman, J.N. (1984). The investigation of magnetic domain structures in thin foils by electron microscopy. J Phys D: Appl Phys 17(4), 623.
Coope, I.D. (1993). Circle fitting by linear and nonlinear least squares. J Opt Theory Appl 76, 381388.
Favia, P., Gonzales, M.B., Simoen, E., Verheyen, P., Klenov, D. & Bender, H. (2011). Nanobeam diffraction: Technique evaluation and strain measurement on complementary metal oxide semiconductor devices. J Electrochem Soc 158(4), H438H446.
Glas, F. (2004). The effect of the static atomic displacements on the structure factors of weak reflections in cubic semiconductor alloys. Philos Mag 84(20), 20552074.
Guerrero, E., Galindo, P., Yáñez, A., Ben, T. & Molina, S.I. (2007). Error quantification in strain mapping methods. Microsc Microanal 13(5), 320328.
Hüe, F., Hÿtch, M., Houdellier, F., Bender, H. & Claverie, A. (2009). Strain mapping of tensiley strained silicon transistors with embedded Si1−y C y source and drain by dark-field holography. Appl Phys Lett 95(7), 073103.
Hÿtch, M., Houdellier, F., Hüe, F. & Snoeck, E. (2008). Nanoscale holographic interferometry for strain measurements in electronic devices. Nature 453, 10861089.
Hÿtch, M.J. & Plamann, T. (2001). Imaging conditions for reliable measurement of displacement and strain in high-resolution electron microscopy. Ultramicroscopy 87(4), 199212.
Jouneau, P.H., Tardot, A., Feuillet, G., Mariette, H. & Cibert, J. (1994). Strain mapping of ultrathin epitaxial ZnTe and MnTe layers embedded in CdTe. J Appl Phys 75(11), 73107316.
Koch, C.T., Özdöl, V.B. & van Aken, P.A. (2010). An efficient, simple, and precise way to map strain with nanometer resolution in semiconductor devices. Appl Phys Lett 96(9), 091901.
Liu, J.P., Li, K., Pandey, S.M., Benistant, F.L., See, A., Zhou, M.S., Hsia, L.C., Schampers, R. & Klenov, D.O. (2008). Strain relaxation in transistor channels with embedded epitaxial silicon germanium source/drain. Appl Phys Lett 93(22), 221912.
Müller, K., Schowalter, M., Rosenauer, A., Rubel, O. & Volz, K. (2010). Effect of bonding and static atomic displacements on composition quantification in In x Ga1−x N y As1−y . Phys Rev B 81(7), 075315.
Ploessl, R., Chapman, J.N., Thompson, A.M., Zweck, J. & Hoffmann, H. (1993). Investigation of the micromagnetic structure of cross-tie walls in permalloy. J Appl Phys 73(5), 24472452.
Prewitt, J.M.S. (1970). Object Enhancement and Extraction, pp. 75149. New York: Academic Press.
Robertson, M.D., Corbett, J.M., Webb, J.B., Jagger, J. & Currie, J.E. (1995). Elastic strain determination in semiconductor epitaxial layers by HREM. Micron 26(6), 521537. (Papers presented at the 22nd Annual Meeting of the Microscopical Society of Canada/Societe de Microscopie du Canada.)
Rosenauer, A., Fischer, U., Gerthsen, D. & Förster, A. (1998). Composition evaluation by lattice fringe analysis. Ultramicroscopy 72, 121133.
Rosenauer, A., Gerthsen, D., Dyck, D.V., Arzberger, M., Böhm, G. & Abstreiter, G. (2001). Quantification of segregation and mass transport in In x Ga1−x As/GaAs Stranski-Krastanow layers. Phys Rev B 64(24), 245334.
Rosenauer, A., Gerthsen, D. & Potin, V. (2006). Strain state analysis of InGaN/GaN sources of error and optimized imaging conditions. Phys Status Solidi A 203(1), 176184.
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(9), 11711182.
Rosenauer, A. & Schowalter, M. (2007). STEMSIM—A new software tool for simulation of STEM HAADF Z-contrast imaging. In Springer Proceedings in Physics, Vol. 120, Cullis, A.G. & Midgley, P.A. (Eds.), pp. 169172. Berlin: Springer.
Rosenauer, A., Schowalter, M., Glas, F. & Lamoen, D. (2005). First-principles calculations of 002 structure factors for electron scattering in strained In x Ga1−x As. Phys Rev B 72, 085326.
Tillmann, K., Lentzen, M. & Rosenfeld, R. (2000). Impact of column bending in high-resolution transmission electron microscopy on the strain evaluation of GaAs/InAs/GaAs heterostructures. Ultramicroscopy 83(1-2), 111128.
Uesugi, F., Hokazono, A. & Takeno, S. (2011). Evaluation of two-dimensional strain distribution by STEM/NBD. Ultramicroscopy 111(8), 995998.
Usuda, K., Numata, T. & Takagi, S. (2005). Strain evaluation of strained-Si layers on SiGe by the nano-beam electron diffraction (NBD) method. Mater Sci Semicond Process 8(1-3), 155159.
Waller, I. (1927). Die Einwirkung der Wärmebewegung der Kristallatome auf Intensität, Lage und Schärfe der Röntgenspektrallinien. Ann Phys 83, 153183.
Yu, W. & Mader, W. (2010). Displacement field measurement of metal sub-lattice in inversion domains of indium-doped zinc oxide. Ultramicroscopy 110(5), 411417.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Microscopy and Microanalysis
  • ISSN: 1431-9276
  • EISSN: 1435-8115
  • URL: /core/journals/microscopy-and-microanalysis
Please enter your name
Please enter a valid email address
Who would you like to send this to? *



Altmetric attention score

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed