3.1.5 High Concentration Effects

  Due to the increase of implantation doses in shallow junction engineering, heavily doped silicon forms unactivated aggregates of particles, which are known as precipitates and clusters. While clusters are restricted to specific configurations of atoms neglecting any crystal properties, precipitates can host thousands of atoms and form second phase regions. The classical interpretation of these high concentration effects is that at a certain temperature only a limited amount of the dopants is able to dissolve on substitutional sites within the silicon crystal. Dopants above the solubility limit form precipitates or clusters. Precipitates are electrically inactive and immobile, where clusters are assumed to be partially active. It is not clear yet, whether to favor a clustering or precipitation model for certain dopant species. Recently, Baccus proposed a clustering model for boron, where the clusters are modeled to be inactive but mobile [Bac93]. The cluster formation process is given by (3.1-32), where is the clustered species composed of interstitial dopant and substitutional dopant atoms.

 

Also Solmi published a precipitation model where he suggested inactive mobile clusters [Sol90]. The classical formulation of clustering assumes unactivated and immobile clusters, composed of impurity atoms and electrons (3.1-33).

 

The total impurity concentration is split up in two parts. The first one comprising the active and mobile dopants is assumed to diffuse strongly at the slope of the profile, while no diffusion is occurring in the regions where clusters are located. The second part consisting of inactive and immobile clusters interacts with the active part by an exchange mechanism. The clustering model is based on mass-action relationships between the active and the cluster state and, hence, variable solubility limits are given, where precipitation models are using a fixed solubility limit, which means local equilibrium is assumed between these two streams. Most researchers, modeling high concentration arsenic profiles, prefer the clustering approach [Gue82] [Tsa80].

Finally, cluster and precipitation phenomena are still under investigations and an area of interest. In Section 4.3 we give details on a clustering model for arsenic and boron.