Calculated PL lifetimes of Si nanowires: the effect of a dispersion in the crystallographic orientations X. Zianni *, A.G. Nassiopoulou IMEL/NCSR ‘Demokritos’, P.O. Box 60228, 153 10 Aghia Paraskevi, Athens, Greece Abstract The photoluminescence (PL) lifetimes have been calculated within effective mass approximation for Si nanowires with a rectangular cross section as a function of their size and their crystallographic direction. Both direct and indirect transitions are found. More than one subband can contribute to the PL lifetime. Depending on the crystallographic direction of the wires, the calculated lifetimes range between microseconds to milliseconds at room temperature. The distribution of the magnitudes of the PL lifetimes assuming a Gaussian distribution for the crystallographic orientations of the quantum wires is discussed. # 2003 Elsevier Science B.V. All rights reserved. Keywords: 78.67.Lt; 78.55.Mb; 73.21.Hb 1. Introduction The observed PL of porous Si stimulated a lot of research on Si nanostructures. Porous Si has been modeled as a system of quantum dots and/or wires. The theoretical investigation of such systems has given a lot of insight in the physics and in the properties of this material [1  /7], while the experimental investigation of different systems containing Si quantum dots or nano- wires have been investigated so as the intrinsic proper- ties due to dots or wires have been demonstrated [8  /12]. The calculations on Si nanostructures have been ex- tended to the investigation of quantum wells, quantum wires and quantum dots. A widening of the band gap from the near-infrared wavelength region to and beyond the visible range by decreasing the sizes from a few nanometers to below 1 nm has been obtained from these calculations. Furthermore, an enhancement of the di- pole matrix element responsible for the radiative transi- tions is found. Both direct and indirect band gap have been reported. Most calculations are restricted to particular cases of geometries and sizes of the dots and of the wires. Effective mass approximation (EMA) can be helpful at this stage since within its framework continuous values can be used for the structural para- meters. The predictions of EMA for the energy band structure of electrons in Si quantum wires, have been discussed in detail in Ref. [13] where the findings of EMA are also compared with results of more sophisti- cated calculations. The implications of the features of the electron band structure on the spontaneous emission have been discussed in Ref. [14]. Here, we discuss the effect of direct and indirect transitions on the behavior of the PL lifetime in Si quantum wires with dimensions in the range of a few nanometers. 2. Model We consider free standing, infinitely long and homo- geneous quantum wires of rectangular cross section. We define the wire direction in a system of coordinates (x , y , z ), that is defined as follows: the z axis is along the [001] direction and the x and y axes are rotated anticlockwise by an angle u relative to the [100] and [010] directions, respectively. The quantum wire infinite length is along the y -axis. Electron and hole eigenstates are obtained by solving Schro ¨ndinger equation. An infinitely deep confining potential has been assumed for electrons and holes in the quantum wires. In Si quantum wires, the six valleys of the minimum of the conduction band of Si are not equivalent and each set of * Corresponding author. Tel.:  /30-1-650-3245; fax:  /30-1-651- 1723. E-mail address: xzianni@imel.demokritos.gr (X. Zianni). Materials Science and Engineering B101 (2003) 242  /245 www.elsevier.com/locate/mseb 0921-5107/03/$ - see front matter # 2003 Elsevier Science B.V. All rights reserved. doi:10.1016/S0921-5107(02)00671-2