Controlled Growth of Silicon Nanocrystals in a Plasma Reactor Holger Vach and Quentin Brulin Laboratoire de Physique des Interfaces et des Couches Minces, CNRS - Ecole Polytechnique, 91128 Palaiseau, France (Received 4 February 2005; revised manuscript received 21 June 2005; published 13 October 2005) Using a powerful multilevel simulation approach, we ‘‘visualize’’ the complete growth dynamics of hydrogenated silicon nanostructures under realistic experimental conditions of a plasma reactor. For the early stages of the synthesis, we demonstrate for the first time how precise control of atomic hydrogen not only permits one to choose between the production of amorphous and crystalline nanoparticles, but also to ‘‘steer’’ the growth toward the formation of elementary ‘‘building blocks’’ for the synthesis of hexagonal silicon nanowires. DOI: 10.1103/PhysRevLett.95.165502 PACS numbers: 81.10.Bk, 61.46.+w, 81.05.Zx, 81.07.Bc In a world of ever shrinking dimensions of electronic devices, crystalline silicon nanoparticles are often at the origin of many new technological breakthroughs [1–3]. Plasma enhanced chemical vapor deposition presents one efficient way of industrial production of those nanopar- ticles [4,5]. The incorporation of plasma-generated nano- crystals in an amorphous matrix has recently been shown to add long-time stability to the outstanding characteristics of polymorphous, thin film solar cells [6]. The atomic scale mechanisms leading to the necessary nanocrystal forma- tion, however, are far from understood, preventing large- scale applications. Pure ab initio molecular dynamics simulations might be considered as the most powerful tool to elucidate the details of the growth dynamics of nanometric systems on an atomic level. Unluckily, how- ever, those calculations are often limited to relatively short simulation times and to quite small systems due to their extensive use of computer power. Therefore, we present here an alternative, multilevel simulation approach that leads to a complete understanding of the physics behind the silicon nanoparticle growth and crystallization under realistic experimental plasma conditions. As an example, we derive the ideal plasma conditions for the formation of elementary nanowire (NW) nuclei. At the lowest level of approximation, we use fluid model calculations to obtain a realistic description of our experi- mentally employed silane plasma [7]. Specifically, those calculations reveal that the interacting atomic and molecu- lar species have room temperature energy distributions in the plasma, that the concentration of SiH 4 molecules is about 50 times less than that of molecular hydrogen, but roughly 1000 times higher than for SiH 3 radicals and about 10 times higher than for atomic hydrogen; all other pos- sible plasma species are expected to be negligible. Those results are then employed as input for our quan- tum molecular dynamics simulations. At this second level of approximation, we routinely follow the individual tra- jectories of all involved atoms with a time resolution of 0.01 fs for at least 100 ps; for the thermal stability study of the proposed NW seeds, we extended this time to 1 ns. Each trajectory is numerically determined from Newton’s equations of motion based on the sum of all forces acting on a given atom due to its interaction with all the other atoms using Gear’s fifth-order predictor-corrector algo- rithm [8]. For the evaluation of the necessary forces, the electronic Schro ¨dinger equation is solved using the semi- empirical PM3 method [9] at each time step; i.e., instead of explicitly solving the integrals necessary for the evaluation of quantum mechanical exchange correlation terms, this methods is based on empirical parameters that are derived from experimental data and that permit to reproduce the available values measured for atomic bond lengths and angles as well as for dipole moments and enthalpies. The excellent agreement between results obtained with this method and those given by both experimental reaction studies and high level ab initio calculations has previously been demonstrated for the silicon-hydrogen system [10,11]. While those previous studies were limited to the reaction dynamics of only three atoms, we here employ the same method to investigate the formation dynamics of nanometric structures. Because of its exponential scaling of computational time with particle number, however, our method is presently limited to particles with less than 25 silicon atoms even using state-of-the-art computers. Never- theless, this computational limit permits us to simulate the growth dynamics of particles with a diameter of about 1 nm and, incidentally, there is experimental evidence that nano- crystals of this size do participate in the thin film properties of polymorphous solar cells [12]. For each experimental condition, twenty trajectories are calculated with randomly chosen initial conditions to assure good statistical sam- pling. At the highest level of theory, we then use first- principles electronic structure calculations to optimize par- ticle structures resulting from our molecular dynamics simulations to determine their physical, chemical and op- tical properties. From the molecular dynamics simulations, we obtain ‘‘cartoons’’ of individual atomic snapshots unveiling the details of the underlying reaction dynamics that are still invisible to the eye of the experimentalist. Moreover, the present simulation technique permits us to discover real- istic and possibly new atomic structures since most former PRL 95, 165502 (2005) PHYSICAL REVIEW LETTERS week ending 14 OCTOBER 2005 0031-9007= 05=95(16)=165502(4)$23.00 165502-1  2005 The American Physical Society