A Model for Boron T.E.D. in Silicon:
Full Couplings of Dopant with Free and Clustered Interstitials

F. Boucard1,2,3, D. Mathiot1, E. Guichard2, and P. Rivallin3
1 Laboratoire PHASE-CNRS, 23 rue du Loess, F-67037 Strasbourg Cedex 2, France
2 SILVACO DATA SYSTEMS , 55, rue Blaise Pascal, F-38330 Montbonnot, France
3 LETI-CEA, 17 Av. des Martyrs F-38054 Grenoble cedex 9, France



In this contribution we present a model for transient enhanced diffusion of boron in silicon. This model is based on the usual pair diffusion mechanism including non-equilibrium reactions between the dopant and the free point defects, taking into account their various charge states. In addition to, and fully coupled with the dopant diffusion we model the growth and dissolution of the interstitials and boron interstitials clusters associated with the anneal of the self-interstitial supersaturation created by the implantation step. It is thus possible to simulate a rather large set of experimental conditions, from conventional predeposition steps, to RTA after low energy implantation.



One of the most important challenges in developing ULSI technology today is to shrink device sizes to their limit. Each generation requires a large effort in research and development, where technological computer aided design (TCAD) can play a key role. Ion implantation is the common technique used for doping advanced silicon devices in microelectronics. However this technique induces a huge supersaturation of point defects in the Si crystal which leads to an anomalous broadening of the dopant profile during the high temperature activation anneal. This phenomenon, known as transient enhanced diffusion (TED) is particularly noticeable and embarrassing for boron diffusion, where it is a serious issue for the formation of the ultra shallow junctions needed for next generation of devices. It is also now well established that TED is strongly correlated with the evolution of the self-interstitial supersaturation governed by the nucleation and evolution, during the high temperature anneal, of a variety of extended defects structures like boron interstitial clusters (BIC) [1] or interstitials clusters (IC) [2]. Thus, predictive process modeling, needed for deep submicron MOSFET technologies, requires the development of accurate diffusion models taking into account the full set of interactions between the dopant and the point or extended defects (clusters). The purpose of this contribution is to show that it is possible to extend the usual dopant pair diffusion model to take into account these interstitial-related clusters. Special attention is paid on the fact that the "new" model is fully consistent with the equilibrium "normal" model.


Basic Diffusion Mechanism

As a starting point of our modeling effort we used an extension of the basic dopant pair diffusion model proposed several years ago by one of us [3]. Briefly, the basic idea of this model is that isolated substitutional boron atoms (BS) are immobile. The dopant diffusion occurs only via the diffusion of boron / self-interstitial (BI) and (to a less extend) of boron / vacancy (BV) pairs. However, in the present work, we do not assume local equilibrium between the pairs and their components. As previously, we considered all the possible charge states of the free defects and of the pairs, the relative concentrations of which depend on the local Fermi level position. Since we want to be able to handle experimental cases where, as after ion implantation, the defect concentrations are of the same order of magnitude or even higher than the dopant concentration, the concentrations of all the charged species (dopant, free point defects, pairs and clusters) are accounted for in the neutrality equation used to compute the electron concentration. Nevertheless, since electronic exchanges are extremely faster than atomic reactions, we assume that the various charge states of a given species are always in local equilibrium, and thus, in order to minimize the number of equations, we explicitly describe only one reaction path for the formation of each pair, the other charge states being consistently computed through the position of the defect related deep level. The pairing reactions between the dopant and point-defects explicitly considered in the present work are the following :


The evolution of the boron and free defect concentrations are then given by the following set of continuity equations :


where the various fluxes (JX) include built-in field drift effects on charged species and RI/V account for the bimolecular recombination between self-interstitials (I) and vacancies (V) [3]. The additional (G-R)In and (G-R)BIC terms account for the generation or consumption of the various species due to the interstitial-related clusters formation and dissolution as described in the following sections.

From these continuity equations solved by PROMIS [5], boron profiles can be theoretically calculated in any experimental situation if appropriate initial conditions are assumed for the point defects. As a first indication of the ability of our model to handle the complex couplings between boron and the free point defects, we show on Figure1 the results of the simulation of conventional predeposition steps (diffusion with a constant surface concentration), where the initial concentrations of the defects are assumed to have their equilibrium values. For this specific case the (G-R) terms linked to the interstitial-related clusters evolution vanish, and such simulations can thus be used to fit the basic parameters describing the dopant interactions with the free point defects. As shown on Figure 1, the agreement between the experimental profiles [4] and the simulated ones, with parameters corresponding to a I contribution to the total B diffusion of the order of 85%, is remarkably good.

Figure 1. Comparison between calculated and experimental boron
predeposition profiles. Experimental data are from ref. [4]


Interstitial Clusters

In order to be able to simulate the T.E.D. of boron, the basic pair diffusion model is fully coupled, through generation and recombination terms, to the equations describing the evolution of the point defects in connection with the growth and dissolution of interstitial clusters.

For this purpose we describe the kinetics of the IC's using the model we developed recently for the growth of {311} defects [6]. In this model, a cluster containing n interstitials evolve to a cluster of size n+1 by interaction with a free interstitial in agreement to the following reactions with the corresponding relations describing the time evolution of the various concentrations :


According to [6], the various rate constants are given by

where is the effective capture radius of the defect of size n, is the effective energy barrier that an interstitial must overcome, Ef(n) is the energetic cost for adding one Si atom to a cluster of size n, i.e. the formation energy per I atom in the cluster of size n, is the formation energy for an isolated self-interstitial, is the number of dissociation sites, and is the lattice distance [6].

The validity of the interstitial cluster growth model is tested by comparing its predictions with the experimental data obtained by Cowern et al. [7]. Briefly, this experiment consists in measuring the enhanced diffusivity of two buried boron marker layers induced by a superficial silicon implantation at 40 keV with a dose of 2.10 at/cm. To start the calculation, we used here a simple +1 model to describe the initial self-interstitial concentration induced by the Si implant. In order to obtain the best fit, the values of the various formation energies have to be slightly changed as compared to the initial values proposed by Cowern et al. We think that this is due to the fact that the way we estimate the formation rate constant kn is somewhat different. In our model, this rate constant depends on the current free self-interstitial supersaturation, in such a way that the formation can be reaction limited for small sizes when the I supersaturation has significantly decreased [6]. However, in agreement with Cowern et al., we found that good fits is possible only by considering some stable "magic" sizes, i.e. cluster containing 4 and 8 atoms. For clusters of size larger than 10 we used {311} formation energies tending asymptotically toward 0.67 eV for large values of n, as depicted on Figure 2.

Figure 2. Fitted formation energy per atom included in a cluster of size n


The corresponding calculated curves are given on Figure 3. On Figure 3(a) we show the excellent agreement between the calculated evolution of the self-interstitial supersaturation as compared to the values extracted from the experimental profile broadening. It is emphasized that our approach allows a particularly nice description of the time evolution of the I supersaturation, especially for low thermal budgets. Since our I evolution model is coupled with the B diffusion equations, it is then possible to simulate the corresponding B broadening. The calculated B profiles are shown on Figure 3(b), and exhibit all the features experimentally observed in [7], i.e. the exponential low concentration tail for low thermal budgets evolving to symmetrically broadened profiles for longer times.

Figure 3. Comparison between experimental and calculated I supersaturation (a), and corresponding calculated B profiles corresponding to ref.[7] (b)

Boron Interstitial Cluster Formation

The simulation of Cowern and coworker's experiment presented above is possible without taking into account the boron interstitial complexes formation, because the boron concentration is low enough. However, when a high concentration of free self-interstitials co-exists with a significant boron concentration, even below the solubility limit, as for example when crystalline silicon is implanted with medium doses of boron, the presence of these immobile BIC's are usually invoked to account for the experimental observations, as for example the loss of electrical activity of the dopant. In order to obtain meaningful simulations of the redistribution and activation of implanted B layers, it is thus necessary to model the BIC's formation.

We used here an approach similar to the one used for the IC's, but considering the various possible formation paths : a given cluster can grow or dissolve by the addition or release of a silicon self interstitial or a boron / interstitial pair. In order to reduce the total number of equations to handle, we restricted ourselves to a limited number of BIC's. In absence of any direct experimental data concerning these clusters, we chose the BIC's structures and charge states obtained from a recent ab-initio theoretical calculation [8]. The corresponding formation paths are given on Figure 4. The various kinetics parameters were also computed with the help of the formation and binding energies given in [8].

Figure 4. BIC's reaction paths.


The model parameters were eventually tuned by fitting on the experimental profiles of Pelaz et.al., which correspond to the redistribution of a buried B layer, with a peak concentration in the 10 cm range, following defect creation by a 2.10 cm Si implant, anneal