From point defects to dislocation loops: a comprehensive TCAD model for self-interstitial defects in silicon Ignacio Martin-Bragado and Ibrahim Avci Synopsys Inc. Mountain View, CA 94043, USA Email: nacho@synopsys.com Nikolas Zographos Synopsys Switzerland LLC 8050 Zurich, Switzerland Pedro Castrillo and Martin Jaraiz Departamento de Electronica Universidad de Valladolid 47011 Valladolid, Spain Abstract— An atomistic model for self-interstitial extended defects is presented in this work. Using a limited set of assumptions about the shape and emission frequency of extended defects, and taking as parameters the interstitial binding energies of extended defects versus their size, this model is able to predict a wide variety of experimental results. The model accounts for the whole extended defect evolution, from the initial small irregular clusters to the {311} defects and to the more stable dislocation loops. The model predicts the extended defect dissolution, supersaturation and defect size evolution with time, and it takes into account the thermally activated transformation of {311} defects into dislocation. The model is also used to explore a two-phase exponential decay observed in the dissolution of {311} defects. I. I NTRODUCTION Current technology uses ion implantation as the main process to introduce dopants in silicon. Inherent to this process is the creation of a high amount of point defects, leading to the formation of different defect agglomerates. Their subsequent dissolution during annealing generates a point defect supersaturation that affects the diffusion of the implanted dopants. A thorough understanding of the dissolution kinetics of these defects is needed in order to correctly predict and control the final dopant profile in the deep sub-micron regime. In particular, extra self-interstitials (I) released both from {311} rod- like defects [1] and small clusters [2] cause the Transient Enhanced Diffusion (TED) of commonly used dopants. Four types of self- interstitial extended defects have been detected experimentally in silicon: [3] small irregular clusters, {311} defects, and faulted and perfect dislocation loops (DLs). All of these defects are of extrinsic character, i.e. they are formed with extra Si atoms precipitated as clusters. A study about the smaller precursor clusters that nucleate and grow into {311}’s was reported by Cowern et al. [4]. Based on experimental observations [5], the unfaulting of the {311} defects is the source of the subthreshold DLs in non-amorphized ion-implanted silicon, i.e. the {311} defects can either dissolve or unfault into loops. The total TED depends mainly on the amount of excess interstitials and on the depth at which the defects are formed. This interstitial supersaturation is related to the energetics of the interstitial defects and defects present in the sample [4], [6]. Consequently to correctly account for TED for incomplete anneals, process simulators have to implement predictive models for the evolution of the small clusters, {311} defects and DLs. In particular, the formation of DLs decreases the supersaturation by several orders of magnitude and it will severely affect the dopant profiles after the incomplete annealing. In consequence, the modelling and accurate prediction of the transition from {311} defects to DLs is imperative. A considerable effort, using both continuum [4], [7]–[13] and atomistic [14]–[16] approaches, has been devoted to the understand- ing of the physical mechanisms that control the nucleation, growth and dissolution of such defects. The continuum method however, is limited by the number of equations that can be solved without run- ning into prohibitive CPU demands and/or convergence instabilities. Moreover, it uses some simplifying assumptions about the capture volume, and it makes a continuum treatment of the discrete extended defects. In this work, we have developed a comprehensive extended defect model which accounts for the whole defect evolution: the point defects nucleate into small clusters which will transform into {311} defects which finally can become DLs. The model has been imple- mented in an atomistic kinetic Monte Carlo (kMC) simulator [17] using a single set of parameters to explain all the different simulation conditions. II. PHYSICAL MODEL In our model I s and vacancies are represented as points in a 3D simulation domain, and they are given random jumps at a rate derived from their diffusivities. They can interact with other particles which are found within their capture radius, leading to cluster formation or recombination. The jump distance and the capture radius is always assumed to be the second neighbor’s distance in the silicon lattice. A. Shape Our model assumes the shape of interstitial clusters with size n< 15 interstitials to be irregular. For bigger sizes we rearrange them into the {311} defects and/or faulted DLs according to the crystalline geometry data. The experimental transition size between small clusters and {311} defects is not well known, and the literature establishes a size of n = 10 as a minimum [4], [12] and n = 40 as a maximum [11]. We assume that irregular clusters retain captured point defects at their arrival position. This assumption leads naturally to a roughly spherical shape. On the other hand {311} defects are modeled as parallel stripes (rows) of interstitials lying in one of the twelve orientations, randomly chosen, of a {311} plane. We model the {311} defect shape, following the experimental data [18], as Nrow rows of I s lying on a < 01 ¯ 1 > line with a distance of a/ √ 2 between I s in the same line and N col columns keeping a distance of a √ 22/4 between them, being a =0.543 nm the silicon lattice parameter. We assume that the ratio between length (L) and width (W ) is given by [9] W ≈ √ CL, with C =0.5 nm. Consequently, the length of the defects is L ≈ 0.5 n 2/3 nm, n being the defect size (number of I s). In our model, {311} defects capture any point defect jumping into the capture volume of the particles belonging to the defect. After the capture, the number of N col and Nrow is recalculated, with a small hysteresis to prevent {311} defect reshape due to the emission and capture of the same particle. The transformation of {311} defects into DLs depends on the size of the {311} defects and on the temperature. DL are expected to be more stable than {311} defects beyond a size of about ≈ 350 atoms.