We present a transient enhanced diffusion model for boron valid in a
temperature range from 
to 
. The dopant diffusion is
typically enhanced by several orders of magnitude in high doped regions. The
enhanced diffusion phenomenon is temperature-, depth- and
concentration-dependent in the early stages of the annealing process. Due to
the strongly extrinsic doping conditions clustering occurs. Hence, we set up
a dynamic clustering model for boron, like given by (4.3-16) and
(4.3-17), to model the exchange of dopants between the immobile
clustered and the mobile active dopants. Generally, enhanced diffusion is
caused by point defects above the thermodynamic equilibrium. The large
amount of excess point defects increases the dopant's possiblity for local
exchange processes, like occuring by interstitialcy or vacancy mechanism.
We model the influence of the point defects onto the diffusion behavior of
the mobile species by an enhanced diffusion coefficient, as shown in
(4.3-4), and neglect the details of the dopant/point defect
interactions. The point defect concentrations are assumed to be generated
according to the so called +1-model [Gil91], where the
point defect profiles are proportional to the implanted dopant
distributions.
As long as the point defect concentration is above the according thermal equilibrium concentration, diffusion enhancement is occurring. The time scale of the enhanced diffusion varies strongly with the annealing temperature and appears to be activated with an energy of 3 eV to 5 eV [Gil91]. At the early stage of diffusion there is strong enhancement observed, because the point defects are still in the local vicinity of the dopants. After a certain time the point defects diffused into the bulk and the transient dopant diffusion enhancement decreases. For higher point defect concentrations the diffusivity enhancement persists for a longer time period than for low dose samples [Cow90b]. The only consistent explanation for this phenomenon is interstitial clustering. The interstitial point defects are also forming immobile aggregates within the lattice defect regions and the point defects are emitted continuously during annealing of the damage. This sophisticated process is captured by a static clustering model for the interstitial concentration. As boron is dominated by the interstitialcy diffusion mechanism (see Fig.3.1-3), the vacancy concentration is treated fully mobile. Additionally, there is bulk recombination occurring between interstitials and vacancies, which results in equilibrium conditions for the point defects after sufficiently long damage annealing.
The complete transient enhanced diffusion system for the clustered dopants, the clustered interstitials and the vacancies is given with (4.3-22) to (4.3-27).
The reaction rate coefficient 
represents the recombination
velocity of the charged point defects, where we assume that all charge
states are lumped together to one equilibrium level rate. For the
calculation of the electric field the model disregards the charges caused by
the point defects.
