Dielectric function of germanium nanocrystals between 0.6 and 6.5 eV by spectroscopic ellipsometry M. Mansour a, * , A. En Naciri a , L. Johann a , S. Duguay b , J.J. Grob b , M. Stchakovsky c , C. Eypert c a Laboratoire de Physique des Milieux Denses, 1Bd Arago, 57078 Metz Cedex 3, France b Institut d’Electronique du Solide et des Syste `mes (InESS), 23 rue du Loess, BP 20, 67037 Strasbourg Cedex 2, France c Horiba Jobin Ivon S.A.S, 5 Avenue Arago, 91380 Chilly Mazarin, France Abstract In this work, we report on the study of dielectric function of nanocrystalline germanium (nc-Ge) implanted in a host matrix SiO 2 on a silicon substrate by spectroscopic ellipsometry (SE). The presence of nc-Ge is observed by transmission electron microscopy (TEM). The SE measurements are performed at 708 of angle of incidence in air at room temperature. We observe that the ellipsometric angles j and D change under specific conditions of elaboration. The dielectric function of germanium nanocrystals 3 nc-Ge is extracted using wavelength by wavelength inversion method, without any dispersion law or adjustment parameters. The critical points are determined from the second derivative of the imaginary part of the dielectric function. As expected the significant broadening of the critical points is observed, the E 0 , E 1 , E 1 CD and E 0 0 critical points shift to higher energies, affected by quantum confinement. This implies a significant change in the direct and indirect transitions responsible for the band structure. q 2006 Elsevier Ltd. All rights reserved. 1. Introduction Great research efforts have been focused on the low- dimensional structures of indirect gap materials like silicon and germanium. These nanometric size materials present physical properties radically different from bulk crystals and are potentially interesting for integration in electronic and optoelectronic devices. Hence the interest is much more important to complete the fundamental physical knowledge, and therefore to apply this knowledge in industry. In bulk germanium, the fundamental band gap is indirect and about 0.66 eV. This indirect transition requires phonon– electron interaction which has a very weak probability. In addition, germanium emissions are restricted to the infrared range. However, the strong photoluminescence (PL) in the visible range observed in silicon and recently in germanium nanoparticles (nc-Ge) [1–4] opened fields of investigations to understand physical mechanisms responsible for this effect. The PL, as function of elaboration parameters and size [4,5] was observed by many authors, but the origin of this intense PL remains very controversial. Several studies have explained that change in the structure of nc-Ge compared to the diamond structure of bulk germanium is the origin of the PL in the visible range [6]. Other studies attributed the PL to the defects in a host matrix [7] and quantum confinement effect is also considered as the origin of this PL [8]. Among the different optical methods, spectroscopic ellipsometry is a powerful technique to characterize optical properties and to explore the band structure of nanometric semiconductor through the determination of the complex dielectric function. This technique based on the polarized light is non-destructive and very sensitive. In this paper, we report the study of ellipsometric responses of nanocrystalline germanium resulting from Ge C implantation in a host matrix SiO 2 on a Si substrate. The dielectric function of germanium nanoparticles 3 nc-Ge is determined using wavelength by wavelength numerical inversion method. The discussion of these results is given in terms of the critical points [9]. These points correspond to transitions near the G point of the Brillouin zone (E 0 , E 0 0 ), a long the L direction (E 1 , E 1 CD) and near the X point (E 2 ). The comparison with bulk germanium characteristics is also given. Journal of Physics and Chemistry of Solids 67 (2006) 1291–1294 www.elsevier.com/locate/jpcs 0022-3697/$ - see front matter q 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.jpcs.2006.01.059 * Corresponding author. Fax: C33 38 731 5801. E-mail addresses: mansour@lpli.sciences.univ-metz.fr, mansour@univ- metz.fr (M. Mansour).