Model Parameters



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Next: 3.3 Transformation Method Up: 3.2.4 Rapid Thermal Annealing Previous: RTA Peculiarities

Model Parameters

 

At least some of the parameters in the model equations (3.2-59) - (3.2-69) are well established, namely the dopant diffusivities . For the interstitial diffusivity and equilibrium concentration we take literature values ([Tan85], [Bro87], [Nic89]). For the other parameters (, , , and ) we have additional conditions.

When the equilibrium between boron, boron interstitial pairs and interstitials is established, normal diffusion () has to take place. Then, the effective diffusion coefficient of the total boron concentration can be equated to the well known literature values (cf. Table 3.2-1).

 

 

A somewhat toilsome derivation [Hei91a] yields (3.2-75) for the effective diffusion coefficient . Its comparison with the literature value (3.2-74) gives us additional relations for the product , and thus reduces the number of free parameters. These relations depend on the local concentrations and and are therefore solved for in the program code, rather than modeling the products explicitly.

 

 

 

Likewise, the annihilation rate and the generation rate of the dopant point-defect pairs cannot be modeled completely individually. At point defect equilibrium the generation term (3.2-62) vanishes. Then the ratio of the concentration of boron at interstitial sites to the concentration of boron at substitutional sites assumes its equilibrium value . A reaction rate determines how fast this equilibrium is approached. We model the two parameters and rather than the rates and directly; they are calculated from (3.2-78).

The decay of the transient diffusion enhancement shows a pronounced temperature dependence. Whilst transient diffusion enhancement lasts about one second at it can take several hundred seconds at . For boron the activation energy for the RTA-effect, and thus for , is approximately according to Michel's experiments [Mic89].

 

In consideration of the relations (3.2-74) - (3.2-78) four adjustable model parameters remain. (1) The reaction rate which determines the velocity of the reaction . (2) The ratio which determines the percentage of the boron concentration residing on interstitial sites in the point defect equilibrium state. (3) A guess for the boron interstitial pair diffusivity in order to separate the products which are given by (3.2-74) - (3.2-77). Note, that the diffusion behavior is primarily determined by the product . And (4) the Frenkel-pair constant . The model parameters are given in Table 3.2-7.

 



next up previous contents
Next: 3.3 Transformation Method Up: 3.2.4 Rapid Thermal Annealing Previous: RTA Peculiarities



Martin Stiftinger
Wed Oct 19 13:03:34 MET 1994