-Before discussing the implementation some assumptions and approximations have to be done. Figure \ref{2} shows the stopping powers and carbon concentration profile calculated by TRIM. The depth region we are interested in is between $0-300 \, nm$, the region between surface of the target and start of the continuous amorphous $SiC_x$ layer (from now on called simulation window), where the nuclear stopping power and the implantation profile can be approximated by a linear function of depth. Furthermore the probability of amorphization is assumed to be proportional to the nuclear stopping power. A local probability of amorphization somewhere in the target is composed of three parts, the ballistic, carbon-induced and stress-induced amorphization. The ballistic amorphization is proportional to the nuclear stopping power, as mentioned before. the carbon-induced amorphization is a linear function of the local carbon concentration. the stress-induced amorphization is proportional to the compressive stress apllied by the amorphous neighbours. Thus the probability of a crystalline volume getting amorphous can be calculated as follows,
+Before discussing the implementation some assumptions and approximations have to be done. Figure \ref{2} shows the stopping powers and carbon concentration profile calculated by TRIM. The depth region we are interested in is between $0-300 \, nm$, the region between the surface of the target and the beginning of the continuous amorphous $SiC_x$ layer (from now on called simulation window), where the nuclear stopping power and the implantation profile can be approximated by a linear function of depth. Furthermore the probability of amorphization is assumed to be proportional to the nuclear stopping power. A local probability of amorphization somewhere in the target is composed of three parts, the ballistic, carbon-induced and stress-induced amorphization. The ballistic amorphization is proportional to the nuclear stopping power, as mentioned before. The carbon-induced amorphization is a linear function of the local carbon concentration. The stress-induced amorphization is proportional to the compressive stress apllied by the amorphous neighbours. Thus the probability of a crystalline volume getting amorphous can be calculated as follows,