Eur. Phys. J. AP 4, 11–26 (1998) T HE EUROPEAN P HYSICAL JOURNAL APPLIED PHYSICS c  EDP Sciences 1998 Quantitative analysis of HRTEM images from amorphous materials. I: About the estimation of C s and δ f from HRTEM diﬀractograms H.S. Baik 1 , T. Epicier 1, a , and E. Van Cappellen 2 1 GEMPPM b , INSA de Lyon, Bˆ atiment 502, 69621 Villeurbanne Cedex, France 2 Philips Research Laboratories, P.O. Box 80 000, 5600 JA Eindhoven, The Netherlands Received: 9 January 1998 / Revised: 30 April 1998 / Accepted: 25 June 1998 Abstract. A quantitative high resolution transmission electron microscopy (HRTEM) study of amorphous materials has been undertaken in the study-case of amorphous germanium. The analysis consists in a mod- eling of amorphous germanium, suitable to run multislice calculations, and to simulate HRTEM images, the computed diﬀractograms of which are numerically compared to experimental ones obtained from a through-focus series taken on a dedicated high resolution microscope equipped with a ﬁeld-emission gun. The ﬁnal aim of this work is to quantify the structural information that can be retrieved from HRTEM images of amorphous materials. As a preliminary step, the coeﬃcient of spherical aberration (Cs) of the microscope, as well as the amount of defocus (δf ) of each micrograph have to be known. The aim of the ﬁrst part of this paper is to determine, as precisely as possible, these parameters. A new method is proposed, as an alternative to usual methods based on least-squares ﬁttings of the zeros of the experi- mental diﬀractograms: the theoretical diﬀractograms are computed, and numerically compared, through the minimization of a proﬁle agreement factor depending upon the Cs and δf values, and the thickness of the amorphous ﬁlm, to the experimental ones. The critical steps of this approach are the modeling of the scattering of the amorphous material, and, more drastically, the estimation of the experimental thickness, which inﬂuences signiﬁcantly the values of Cs and δfs. PACS. 61.14.-x Electron diﬀraction and scattering – 61.16.Bg Transmission, reﬂection and scanning electron microscopy (including EBIC) – 61.43.Dq Amorphous semiconductors, metals, and alloys 1 Introduction 1.1 Generalities During the past ten years, an increasing number of studies of amorphous structures have been conducted using high resolution transmission electron microscopy (HRTEM). This technique appears to be a promising tool to investi- gate the structure of non-crystalline materials, owing to its ability to transfer more and more information, be- cause of the improvement of the resolution of the mi- croscopes. Among the numerous studies that have been undertaken recently, one can refer to the modeling of HRTEM images from amorphous materials [1,2], the anal- ysis of crystal/amorphous interfaces [3], the detection of nano-crystallites in amorphous materials [4–6] and the in- vestigation of amorphous thin ﬁlms either by HRTEM [7] or by electron diﬀraction [8]. a e-mail: epicier@cismsun.univ-lyon1.fr b UMR CNRS 5510 The present work is devoted to the structural analysis of a study-case material, i.e. amorphous germanium, by means of high resolution imaging. In the ﬁrst part of this work, attention will be paid to the experimental diﬃculties encountered to measure the coeﬃcient of spherical aberration (C s ) and the amount of defocus δf for each experimental image. Although the usual methods for such measurements are well-known (see next section), it will be seen that they are not accu- rate enough to allow a reliable and quantitative match of HRTEM diﬀractograms from amorphous materials. The second part of this work will be more precisely devoted to the quantitative analysis of the HRTEM images obtained from the amorphous-germanium thin ﬁlm; the aim of this approach is indeed to quantify the structural information that can be retrieved from the experimental micrographs. 1.2 Measuring C s and δf from HRTEM diﬀractograms As a matter of fact, HRTEM studies in materials science require more and more image simulations, because of the