3.3.5.4 Amorphization

If the number of generated point defects is very high a crystalline material undergoes a phase transition to an amorphous state where neither long range nor short range order of the atoms can be found.

A widely used method to model this phase transition is to assume a threshold level for amorphization $\rho_{\alpha}$. An area where the sum of the interstitial concentration $\rho_{I}$ and the vacancy concentration $\rho_{V}$ is above this amorphization threshold level, is considered as being completely amorphous. The point defect concentrations that are required to determine the phase transition can be calculated either by the Follow-Each-Recoil method or by the Kinchin-Pease damage model.

$$\rho_{V} + \rho_{I} > \rho_{\alpha}\;\;\Longrightarrow$$ (3.172)

$$\rho_{V} + \rho_{I} > \rho_{\alpha}\;\;\Longrightarrow$$ (3.173)

If a simulation is performed with a point defect concentration threshold level of $2{\cdot}10^{22}$cm$^{-3}$ simulated amorphous areas in crystalline silicon agree very well with measured amorphization thicknesses for implantations performed at room temperature. Since the generation of amorphous areas strongly depends on the wafer temperature the threshold point defect concentration for amorphization $\rho_{\alpha}$ is only valid for room temperature. In order to determine the amorphization also for a wider temperatures range $\rho_{\alpha}$ had to be modeled as a function of the wafer temperature.