Characterization of asymmetric fragmentation patterns in SFM images of porous silicon A. Ferreira da Silva a, * , R.R. Rosa b , L.S. Roman c , E. Veje d,1 , I. Pepe e a Laborato ´rio Associado de Sensores e Materiais (LAS), Instituto Nacional de Pesquisas Espaciais-INPE Cx. Postal 515, 12201-970, S.J. dos Campos, SP, Brazil b Laborato ´rio de Computc ¸a ˜o e Matema ´tica Aplicada (LAC) Instituto Nacional de Pesquisas Espaciais-INPE Cx. Postal 515, 12201-970, S.J. dos Campos, SP, Brazil c Laboratory of Applied Physics, Department of Physics, Linkoping University, 5-58183 Linkoping, Sweden d Oersted Laboratory, Niels Bohr Institute, Universitetsparken 5 DK-2100 Copenhagen, Denmark e Laborato ´rio de Propriedades Opticas, Instituto de Fı ´sica, Universidade Federal da Bahia 40210-340 Salvador, Ba, Brazil Received 17 May 1999; accepted 3 December 1999 by D.J. Lockwood Abstract Due to possible technological applications in opto-electronic devices, the interest in characterizing porous silicon structure patterns has recently increased. From scanning force microscopy (SFM) we have obtained images of different samples of porous silicon and applied pattern characterization operators on these matrices. In this paper, asymmetric spatial fragmentation in amplitude envelopes of porous silicon samples are characterized by means of a parameter that quantifies the amount of spatial asymmetry in the gradient field. The results show that this method is well suited to characterize silicon porosity quantitatively.  2000 Elsevier Science Ltd. All rights reserved. Keywords: A. Semiconductors; B. Nanofabrications; C. Crystal structure and symmetry; D. Optical properties 1. Introduction Porous silicon (p-Si) has been exposed to a great deal of detailed wide-ranging investigations over the last few years because of its bright visible luminescence even at room temperature (e.g. Refs. [1–21]). Usually, the porous silicon samples are produced by anodic etching of crystalline sili- con (c-Si) wafers in hydrofluoric (HF) acid solution. It has been discussed at length whether the bright photolumines- cence (PL) is of a molecular origin or is related to quantum confinement in nanocrystallites of silicon in the p-Si layer. Indeed, recent experiments have shown that the surface modification procedures have been directed toward improv- ing the material’s optical properties [2,7,13,16]. Much effort has been made to understand the mechanisms underlying this behavior, which is very different from that of c-Si (e.g. Ref. [21]). In fact, it is known that higher porosity silicon exhibits a shift of the spectral position of the visible band to higher threshold energy, from 1.2 to 2.2 eV. This is observed with porosity above 60%, which is achieved by pore enlargement [4,5,13,16,20]. However, the formation mechanism of the pore network is still not well understood. In this paper, different surface structures, that we call canonical samples, are obtained by varying the parameters of anodic etching of c-Si in acid solution. As reported by many authors (e.g. Ref. [3]) one of the main problems in the analysis of these samples is that there are no satisfactory models to explain them and to predict their variations with the different formation parameters (doping level, HF concentration and current density). Focusing on this problem, the objective of this study is to perform a compar- ison among different spatial patterns and then investigate the porosity pattern taking into account a possible structure correlation with absorption energy. For this we apply the so-called asymmetric amplitude fragmentation (AAF) operator [23,24] to images of three typical p-Si samples Solid State Communications 113 (2000) 703–708 0038-1098/00/$ - see front matter  2000 Elsevier Science Ltd. All rights reserved. PII: S0038-1098(99)00557-8 PERGAMON www.elsevier.com/locate/ssc * Corresponding author. Fax: + 55-71-235-5592. 1 Present address: Department of Electric Power Engineering, Technical University of Denmark, Building 325, DK-2800 Lyngby, Denmark. E-mail address: ferreira@las.inpe.br (A. Ferreira da Silva).