George H. Gilmer

PHYSICAL MECHANISMS OF TRANSIENT ENHANCED DOPANT DIFFUSION IN ION-IMPLANTED SILICON

Implanted B and P dopants in Si exhibit transient enhanced diffusion (TED) during annealing which arises from the excess interstitials generated by the implant. In order to study the mechanisms of TED, transmission electron microscopy measurements of implantation damage were combined with B diffusion experiments using doping marker structures grown by molecular-beam epitaxy (MBE). Damage from nonamorphizing Si implants at doses ranging from 5×1012 to 1×1014/cm2 evolves into a distribution of {311} interstitial agglomerates during the initial annealing stages at 670–815 °C. The excess interstitial concentration contained in these defects roughly equals the implanted ion dose, an observation that is corroborated by atomistic Monte Carlo simulations of implantation and annealing processes. The injection of interstitials from the damage region involves the dissolution of {311} defects during Ostwald ripening with an activation energy of 3.8±0.2 eV. The excess interstitials drive substitutional B into electric...

Molecular dynamics investigation of the crystal–fluid interface. VI. Excess surface free energies of crystal–liquid systems

We present the first direct calculation by simulation of the excess surface free energy of a crystal–liquid interface. We perform these calculations on the (111), (100), and (110) interfaces of a truncated Lennard‐Jones face‐centered‐cubic crystal–liquid system at the triple point by the molecular dynamics technique. Bulk crystal and liquid systems are first cleaved and then combined with one another reversibly. The work required to do this is integrated and equals the excess surface Helmholtz (and Gibbs) free energy. The free energies are found to be 0.35±0.02, 0.34±0.02, and 0.36±0.02 (dimensionless units) for the (111), (100), and (110) faces, respectively. The three faces are therefore energetically isotropic within our error bars and the equilibrium form of the crystal is approximately spherical.

Molecular dynamics of surface diffusion. I. The motion of adatoms and clusters

The motion of isolated adatoms and small clusters on a crystal surface is investigated by a novel and efficient simulation technique. The trajectory of each atom is calculated by molecular dynamics, but the exchange of kinetic energy with the crystal lattice is included through interactions with a ’’ghost’’ atom. This atom represents surface atoms of the lattice and is subjected to random and dissipative forces that are related by the fluctuation–dissipation theorem. The diffusion process is characterized by measurements of the velocity autocorrelation function, mean square displacement, directional correlations between hops, and the mean displacement per hop. In addition, the rate of evaporation of single adatoms and the rate of dissociation of clusters are discussed. The diffusion of an isolated adatom is found to be somewhat faster than that predicted by the classical rate theory for an activated process. This effect is a result of diffusion jumps of several atomic diameters that occur preferentially a...

B diffusion and clustering in ion implanted Si: The role of B cluster precursors

A comprehensive model for B implantation, diffusion and clustering is presented. The model, implemented in a Monte Carlo atomistic simulator, successfully explains and predicts the behavior of B under a wide variety of implantation and annealing conditions by invoking the formation of immobile precursors of B clusters, prior to the onset of transient enhanced diffusion. The model also includes the usual mechanisms of Si self-interstitial diffusion and B kick-out. The immobile B cluster precursors, such as BI2 (a B atom with two Si self-interstitials) form during implantation or in the very early stages of the annealing, when the Si interstitial supersaturation is very high. They then act as nucleation centers for the formation of B-rich clusters during annealing. The B-rich clusters constitute the electrically inactive B component, so that the clustering process greatly affects both junction depth and doping level in high-dose implants.

Molecular dynamics investigation of the crystal–fluid interface. I. Bulk properties

Properties of the crystal and liquid phases have been measured for a system of particles interacting through a modified Lennard‐Jones potential. Through constant pressure molecular dynamics, we have evaluated the density and internal energy of these phases at a pressure that approximates that of the vapor phase. The free energy of the crystal is obtained with the Einstein crystal as a reference state, and the liquid free energy is measured relative to the ideal gas. The triple point temperature is obtained. Compressibilities and Gruneisen parameters are obtained at zero temperature and the triple point. Dynamic properties of the supercooled liquid state are also calculated. These results are applied in forthcoming publications which calculate surface excess quantities and dynamic properties of the fcc (111), (100), and (110) faces.

An atomistic simulator for thin film deposition in three dimensions

We describe an atomistic simulator for thin film deposition in three dimensions (ADEPT). The simulator is designed to bridge the atomic and mesoscopic length scales by using efficient algorithms, including an option to speed up surface diffusion using events with multiple diffusion hops. Sputtered particles are inserted and assigned ballistic trajectories with angular distributions appropriate for magnetron sputtering. Atoms on the surface of the film execute surface diffusion hops with rates that depend on the local configuration, and are consistent with microscopic reversibility. The potential energies are chosen to match information obtained from a database of first principles and molecular dynamics (MD) calculations. Efficient computation is accomplished by selecting atoms with probabilities that are proportional to their hop rates. A first implementation of grain boundary effects is accomplished by including an orientation variable with each occupied site. Energies and mobilities are assigned to atom...

Atomistic calculations of ion implantation in Si: Point defect and transient enhanced diffusion phenomena

A new atomistic approach to Si device process simulation is presented. It is based on a Monte Carlo diffusion code coupled to a binary collision program. Besides diffusion, the simulation includes recombination of vacancies and interstitials, clustering and re‐emission from the clusters, and trapping of interstitials. We discuss the simulation of a typical room‐temperature implant at 40 keV, 5×1013 cm−2 Si into (001)Si, followed by a high temperature (815 °C) anneal. The damage evolves into an excess of interstitials in the form of extended defects and with a total number close to the implanted dose. This result explains the success of the ‘‘+1’’ model, used to simulate transient diffusion of dopants after ion implantation. It is also in agreement with recent transmission electron microscopy observations of the number of interstitials stored in (311) defects.

B cluster formation and dissolution in Si: A scenario based on atomistic modeling

A comprehensive model of the nucleation, growth, and dissolution of B clusters in Si is presented. We analyze the activation of B in implanted Si on the basis of detailed interactions between B and defects in Si. In the model, the nucleation of B clusters requires a high interstitial supersaturation, which occurs in the damaged region during implantation and at the early stages of the postimplant anneal. B clusters grow by adding interstitial B to preexisting B clusters, resulting in B complexes with a high interstitial content. As the annealing proceeds and the Si interstitial supersaturation decreases, the B clusters emit Si interstitials, leaving small stable B complexes with low interstitial content. The total dissolution of B clusters involves thermally generated Si interstitials, and it is only achieved at very high temperatures or long anneal times.

Simulation of cluster evaporation and transient enhanced diffusion in silicon

The evaporation of {311} self‐interstitial clusters has recently been linked to the phenomenon of transient enhanced diffusion in silicon. A theory of cluster evaporation is described, based on first‐order kinetic equations. It is shown to give a good account of the data over a range of temperatures. The theory simultaneously explains several of the unexpected features of transient enhanced diffusion, including the apparently steady level of the enhancement during its duration, and the dependence of the duration on implant energy and dose. The binding energy used to match the theory to data is in good agreement with molecular dynamics calculations of cluster stability in silicon.

Carbon in silicon: Modeling of diffusion and clustering mechanisms

Carbon often appears in Si in concentrations above its solubility. In this article, we propose a comprehensive model that, taking diffusion and clustering into account, is able to reproduce a variety of experimental results. Simulations have been performed by implementing this model in a Monte-Carlo atomistic simulator. The initial path for clustering included in the model is consistent with experimental observations regarding the formation and dissolution of substitutional C–interstitial C pairs (Cs–Ci). In addition, carbon diffusion profiles at 850 and 900 °C in carbon-doping superlattice structures are well reproduced. Finally, under conditions of thermal generation of intrinsic point defects, the weak temperature dependence of the Si interstitial undersaturation and the vacancy supersaturation in carbon-rich regions also agree with experimental measurements.