From Si Nanowires to Porous Silicon: The Role of Excitonic Effects Mauro Bruno, 1 Maurizia Palummo, 1 Andrea Marini, 1 Rodolfo Del Sole, 1 and Stefano Ossicini 2 1 European Theoretical Spectroscopy Facility (ETSF), CNR-INFM Institute for Statistical Mechanics and Complexity, CNISM and Dipartimento di Fisica, Universita ´ di Roma ‘‘Tor Vergata,’’ via della Ricerca Scientifica 1, 00133 Roma, Italy 2 CNR-INFM-S ‘‘NanoStructures and BioSystems at Surfaces,’’ and Dipartimento di Scienze e Metodi dell Ingegneria, Universita ` di Modena e Reggio Emilia, via Amendola 2, Padiglione Morselli, I-42100 Reggio Emilia, Italy (Received 27 October 2006; published 17 January 2007) We show that the electronic and optical properties of silicon nanowires, with different size and orientation, are dominated by important many-body effects. The electronic and excitonic gaps, calculated within first principles, agree with the available experimental data. Huge excitonic effects, which depend strongly on wire orientation and size, characterize the optical spectra. Modeling porous silicon as a collection of interacting nanowires, we find an absorption spectrum which is in very good agreement with experimental measurements only when the electron-hole interaction is included. DOI: 10.1103/PhysRevLett.98.036807 PACS numbers: 73.22.f, 78.67.Bf Nanostructuring of semiconductors is a means of devel- oping new electronic and optoelectronic devices. The huge efforts made towards matter manipulation at the nanometer scale have been motivated by the fact that desirable prop- erties can be generated just by changing the system dimen- sion and shape. In particular, after the discovery of visible photoluminescence in porous silicon (PS) and in Si nano- structures [1– 3], the possibility of tuning the optical re- sponse of Si nanosized materials by modifying their size has become one of the most challenging aspects of recent semiconductor research due to their natural compatibility with silicon based technologies [4]. In this realm, Si nano- wires (Si-NWs) constitute an example of one-dimensional structures with remarkable size and orientation dependent absorption and photoluminescence properties. Thin Si- NWs down to about 1 nm diameter have been obtained with growth orientation along the [100], [110], [111], and [112] directions and with a very rich surface chemistry [4 – 9]. Furthermore, together with Si nanocrystals, Si-NWs are used to model the optical and photoluminescence proper- ties of PS [10]. However, despite the large amount of experimental data available, our understanding of the elec- tronic properties of Si-NWs and PS is still almost confined to single-particle calculations done with semiempirical methods [11] or with the ab initio density functional theory (DFT), usually within the local density approximation (LDA) [12]. As a result the measured electronic gaps for various Si-NWs are larger than the LDA gaps by almost 50%. More importantly, the role of the electron-hole (e-h) interaction, neglected within any independent-particle ap- proach, is typically treated within the simple effective mass approximation (EMA) [13]. A similar scenario has been found in analogous one-dimensional systems [14], such as nanotubes [15 –17] and molecular organic chains [18,19], where, through first-principles excited-states calculations, the optical spectra are now quantitatively explained in terms of strong excitonic effects in a confined geometry. On the other hand, the ab initio optical properties of Si- NWs and PS have been calculated up to now at the level of the random-phase approximation (RPA), i.e., within the independent-particle approximation [20,21]. There exists a complete collection of optical, electronic, and photoluminescence experimental results for Si-NWs and PS that needs a consistent and sound interpretation in terms of a parameter-free theory. This is the goal of the present Letter. We show that only a fully microscopic, ab initio theory that correctly includes self-energy correc- tions and excitonic effects, well beyond the DFT-LDA, correctly explains the size-dependent experimental gaps in Si-NWs. Moreover, we show that the present results reproduce the photoluminescence gaps and the optical absorption of PS, questioning the interpretation of its opti- cal data only in terms of Si nanocrystals. Calculation details. —We first compute the ground-state properties (atomic configurations and single-particle states) using the DFT-LDA of nine Si-NWs, with different sizes and orientations. As a second step, we include self- energy corrections in the GW (where G is the Green function and W is the screened Coulomb interaction) ap- proximation [22] to obtain the quasiparticle (QP) energies, and finally we describe the excitonic effects by solving the Bethe-Salpeter equation (BSE) [23] in the Bloch-space representation [24]. In Fig. 1 we compare the QP electronic gaps with the experimental data obtained by Ma et al. [7] through scan- ning tunneling spectroscopy, for different Si-NWs (grown along the [112] and [110] directions) with diameters rang- ing from 1.3 to 7 nm [7]. All the experimental gaps, although 50% larger than the LDA values, fall within our [100] and [110] theoretical QP curves, which represent the two limiting cases in terms of quantum confinement effects [14]. By fitting the QP band gaps E g with a function of the effective wire diameter d, E g;bulk  const 1=d  (where E g;bulk is the bulk gap value and  is the scaling exponent) we find orientation dependent values for  (see Fig. 1). These values are, in any case, smaller than 2, the value PRL 98, 036807 (2007) PHYSICAL REVIEW LETTERS week ending 19 JANUARY 2007 0031-9007= 07=98(3)=036807(4) 036807-1  2007 The American Physical Society