### 5.6.3.1 The Model for Cluster Formation and Dissolution

In [109] the equation describing interstitial cluster kinetics is described as

 (5.17)

where denotes the interatomic spacing, the capture radius expressed in units of the interatomic spacing, the interstitial diffusivity, the concentration of unclustered interstitials, the concentration of clustered interstitials, the time, the annealing temperature in Kelvin, and the Boltzmann constant. TSUPREM-IV uses a general clustering model that uses many of the models proposed in literature as subsets. The main formula for the change of the concentration of clustered interstitials is [13]

 (5.18)

where denotes an equilibrium concentration of interstitials. All other symbols of (5.18) are parameters that need to be adjusted. , , and are the reactions constants which have the form
 (5.19) (5.20) (5.21)

with coefficients , , and . Since the coefficients are all positive the first two terms of (5.18) describe the formation of clusters whereas the last term describes its dissolution. The term describes the joining of two clusters5.7. Therefore, the parameter values and are expected to be . The second term, , describes the case where an unclustered interstitial joins a cluster. A value of for and is assumed.

2003-03-27