Hostname: page-component-8448b6f56d-dnltx Total loading time: 0 Render date: 2024-04-16T15:41:08.402Z Has data issue: false hasContentIssue false
  • English
  • Français

Influence of Static Atomic Displacements on Composition Quantification of AlGaN/GaN Heterostructures from HAADF-STEM Images

Published online by Cambridge University Press:  10 July 2014

Marco Schowalter ,
Ingo Stoffers ,
Florian F. Krause ,
Thorsten Mehrtens ,
Knut Müller ,
Malte Fandrich ,
Timo Aschenbrenner ,
Detlef Hommel  and
Andreas Rosenauer
Marco Schowalter*
Affiliation:
Institut für Festkörperphysik, Universität Bremen, Otto-Hahn-Allee 1, 28359 Bremen, Germany
Ingo Stoffers
Affiliation:
Institut für Festkörperphysik, Universität Bremen, Otto-Hahn-Allee 1, 28359 Bremen, Germany
Florian F. Krause
Affiliation:
Institut für Festkörperphysik, Universität Bremen, Otto-Hahn-Allee 1, 28359 Bremen, Germany
Thorsten Mehrtens
Affiliation:
Institut für Festkörperphysik, Universität Bremen, Otto-Hahn-Allee 1, 28359 Bremen, Germany
Knut Müller
Affiliation:
Institut für Festkörperphysik, Universität Bremen, Otto-Hahn-Allee 1, 28359 Bremen, Germany
Malte Fandrich
Affiliation:
Institut für Festkörperphysik, Universität Bremen, Otto-Hahn-Allee 1, 28359 Bremen, Germany
Timo Aschenbrenner
Affiliation:
Institut für Festkörperphysik, Universität Bremen, Otto-Hahn-Allee 1, 28359 Bremen, Germany
Detlef Hommel
Affiliation:
Institut für Festkörperphysik, Universität Bremen, Otto-Hahn-Allee 1, 28359 Bremen, Germany
Andreas Rosenauer
Affiliation:
Institut für Festkörperphysik, Universität Bremen, Otto-Hahn-Allee 1, 28359 Bremen, Germany
*
*Corresponding author.schowalter@ifp.uni-bremen.de
Get access

Abstract

In an earlier publication Rosenauer et al. introduced a method for determination of composition in AlGaN/GaN heterostructures from high-angle annular dark field (HAADF) images. Static atomic displacements (SADs) were neglected during simulation of reference data because of the similar covalent radii of Al and Ga. However, SADs have been shown (Grillo et al.) to influence the intensity in HAADF images and therefore could be the reason for an observed slight discrepancy between measured and nominal concentrations. In the present study parameters of the Stillinger–Weber potential were varied in order to fit computed elastic constants, lattice parameters and bonding energies to experimental ones. A reference data set of HAADF images was simulated, in which the new parameterization was used to account for SADs. Two reference samples containing AlGaN layers with different Al concentrations were investigated and Al concentrations in the layers determined based on the new data set. We found that these concentrations were in good agreement with nominal concentrations as well as concentrations determined using alternative techniques such as strain state analysis and energy dispersive X-ray spectroscopy.

Keywords

composition quantificationstatic atomic displacementsSTEMHAADFZ-contrastsemiconductors
Type
Materials Applications
Information
Microscopy and Microanalysis , Volume 20 , Issue 5 , October 2014 , pp. 1463 - 1470
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.)

Footnotes

a

M. Schowalter and I. Stoffers contributed to the present work in equal part and share first-authorship.

References

Cordero, B., Gomez, V., Platero-Prats, A.E., Reves, M., Echeverria, J., Cremades, E., Barragan, F. & Alvarez, S. (2008). Covalent radii revisited. Dalton Trans, 2832–2838.CrossRefGoogle ScholarPubMed
Forbes, B., D'Alfonso, A., Findlay, S., Van Dyck, D., LeBeau, J., Stemmer, S. & Allen, L. (2011). Thermal diffuse scattering in transmission electron microscopy. Ultramicroscopy 111(12), 1670–1680.CrossRefGoogle ScholarPubMed
Glas, F. (2004). The effect of the static atomic displacements on the structure factors of weak reflections in cubic semiconductor alloys. Phil Mag 84, 2055.CrossRefGoogle Scholar
Grieb, T., Müller, K., Fritz, R., Schowalter, M., Neugebohrn, N., Knaub, N., Volz, K. & Rosenauer, A. (2012). Determination of the chemical composition of GaNAs using STEM HAADF imaging and STEM strain state analysis. Ultramicroscopy 117, 15–23.CrossRefGoogle ScholarPubMed
Grillo, V., Carlino, E. & Glas, F. (2008). Influence of the static atomic displacement on atomic resolution z-contrast imaging. Phys Rev B 77(5), 054103.CrossRefGoogle Scholar
Iwama, S., Hayakawa, K. & Arizumi, T. (1982). Ultrafine powders of TiN and AlN produced by a reactive gas evaporation technique with electron beam heating. J Crystal Growth 56(2), 265–269.CrossRefGoogle Scholar
Keating, P.N. (1966). Effect of invariance requirements on the elastic strain energy of crystals with application to the diamond structure. Phys Rev 145(2), 637–645.CrossRefGoogle Scholar
Klenov, D. & Stemmer, S. (2006). Contributions to the contrast in experimental high-angle annular dark-field images. Ultramicroscopy 106, 889–901.CrossRefGoogle Scholar
Klenov, D.O., Findlay, S.D., Allen, L.J. & Stemmer, S. (2007). Influence of orientation on the contrast of high-angle annular dark-field images of silicon. Phys Rev B 76, 014111.CrossRefGoogle Scholar
Kresse, G. & Furthmüller, J. (1996). Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Phys Rev B 54(16), 11169–11186.CrossRefGoogle ScholarPubMed
LeBeau, J.M. & Stemmer, S. (2008). Experimental quantification of annular dark-field images in scanning transmission electron microscopy. Ultramicroscopy 108(12), 1653–1658.CrossRefGoogle ScholarPubMed
Lei, H., Chen, J., Jiang, X. & Nouet, G. (2009). Microstructure analysis in strained-InGaN/GaN multiple quantum wells. Microelectronics J 40(2), 342–345.CrossRefGoogle Scholar
Mehrtens, T., Bley, S., Satyam, P.V. & Rosenauer, A. (2012). Optimization of the preparation of GaN-based specimens with low-energy ion milling for (S)TEM. Micron 43(8), 902–909.CrossRefGoogle ScholarPubMed
Mehrtens, T., Schowalter, M., Tytko, D., Choi, P., Raabe, D., Hoffmann, L., Jünen, H., Rossow, U., Hangleiter, A. & Rosenauer, A. (2013). Measurement of the indium concentration in high indium content InGaN layers by scanning transmission electron microscopy and atom probe tomography. Appl Phys Lett 102(13), 132112.CrossRefGoogle Scholar
Molina, S., Sales, D., Galindo, P., Fuster, D., González, Y., Aln, B., González, L., Varela, M. & Pennycook, S. (2009). Column-by-column compositional mapping by Z-contrast imaging. Ultramicroscopy 109(2), 172–176.CrossRefGoogle ScholarPubMed
Muller, D.A., Edwards, B., Kirkland, E.J. & Silcox, J. (2001). Simulation of thermal diffuse scattering including a detailed phonon dispersion curve. Ultramicroscopy 86(34), 371–380.CrossRefGoogle ScholarPubMed
Pennycook, S. & Jesson, D. (1991). High-resolution Z-contrast imaging of crystals. Ultramicroscopy 37(14), 14–38.CrossRefGoogle Scholar
Plimpton, S. (1995). Fast parallel algorithms for short-range molecular dynamics. J Comput Phys 117(1), 1–19.CrossRefGoogle 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 AlxGa1−xN/GaN using high-angle annular dark-field images. Ultramicroscopy 109(9), 1171–1182.CrossRefGoogle Scholar
Rosenauer, A., Mehrtens, T., Müller, K., Gries, K., Schowalter, M., Satyam, P.V., Bley, S., Tessarek, C., Hommel, D., Sebald, K., Seyfried, M., Gutowski, J., Avramescu, A., Engl, K. & Lutgen, S. (2011). Composition mapping in InGaN by scanning transmission electron microscopy. Ultramicroscopy 111, 1618.CrossRefGoogle ScholarPubMed
Rosenauer, A. & Schowalter, M. (2007). STEMSIM-a new software tool for simulation of STEM HAADF Z-contrast imaging. In Springer Proceedings in Physics, Cullis A.G. & Midgley P.A. (Eds.), vol. 120, pp. 169–172). Dordrecht, Netherlands: Springer.Google Scholar
Ruterana, P., Barbaray, B., Béré, A., Vermaut, P., Hairie, A., Paumier, E., Nouet, G., Salvador, A., Botchkarev, A. & Morkoç, H. (1999). Formation mechanism and relative stability of the $11\bar{2}0$ stacking fault atomic configurations in wurtzite (Al,Ga,In) nitrides. Phys Rev B 59(24), 15917–15925.CrossRefGoogle Scholar
Schowalter, M., Rosenauer, A., Titantah, J.T. & Lamoen, D. (2009). Temperature-dependent Debye-Waller factors for semiconductors with the wurtzite-type structure. Acta Crystallogr Sect A 65(3), 227–231.CrossRefGoogle ScholarPubMed
Stillinger, F.H. & Weber, T.A. (1985). Computer simulation of local order in condensed phases of silicon. Phys Rev B 31(8), 5262–5271.CrossRefGoogle ScholarPubMed
Tersoff, J. (1988). Empirical interatomic potential for silicon with improved elastic properties. Phys Rev B 38, 9902.CrossRefGoogle ScholarPubMed
Van Aert, S., Verbeeck, J., Erni, R., Bals, S., Luysberg, M., Van Dyck, D. & Van Tendeloo, G. (2009). Quantitative atomic resolution mapping using high-angle annular dark field scanning transmission electron microscopy. Ultramicroscopy 109(10), 1236–1244.CrossRefGoogle ScholarPubMed
Van Dyck, D. (2009). Is the frozen phonon model adequate to describe inelastic phonon scattering? Ultramicroscopy 109(6), 677–682.CrossRefGoogle ScholarPubMed
Wright, A.F. (1997). Elastic properties of zinc-blende and wurtzite AlN, GaN, and InN. J Appl Phys 82(6), 2833–2839.CrossRefGoogle Scholar
Zhang, Z., Chatterjee, A., Grein, C., Ciani, A.J. & Chung, P.W. (2011). Atomic-scale modeling of InxGa1−xN quantum dot self-assembly. J Vac Sci Techn B 29(3), 03C133.CrossRefGoogle Scholar