Figure 8. Repartition of P between substitutional sites and vacancy complexes, density of mono-vacancies and free electron concentration as a function of the total number of vacancies present in the sample (Ptotal = 2x1020 cm-3, no fluorine). The intersection between the calculated free electron concentration, and the experimentally observed n nmax of ~5x1019 cm-3 for = 5x1019 cm-3 indicates that this is a reasonable estimate of the residual vacancy Vtotal concentration in the sample after implantation and RTA at 600°C. Figure 8 shows the result of this model in the absence of fluorine for a temperature of 600°C and a chemical concentration of phosphorus corresponding to its solid solubility in germanium (2x1020 cm-3), treating the total number of vacancies as an unknown variable. For a small number of vacancies, most phosphorus atoms are substitutional, and the activation level is close to 100%. However, as the number of vacancies increase, so does the number of PV associates, resulting in a drop in the free carrier concentration. When the free electron concentration becomes too low, the formation of PV centers becomes unfavorable, and mono-vacancies dominate the vacancy population. Experimentally, the free carrier concentration is capped at 5x1019 cm-3, which for a phosphorus concentration of 2x1020 cm-3 corresponds to a total concentration of vacancies of 5x1019 cm-3 (intersection of the experimental and modeled free carrier concentrations in Figure 8), which serves as an approximation of the number of vacancies present in the material. Next, we model how the fluorine dose influences the free carrier concentration, for example in Figure 9, the free electron concentration is plotted as a function of the fluorine dose, for total vacancy concentrations of 2.5x1019 cm-3, 5x1019 cm-3 and 7.5x1019 cm-3, respectively. Figure 9. Free electron concentration versus fluorine concentration, for different vacancy concentrations, at 600°C. The influence of fluorine on the activation of phosphorus scales linearly with the dose until the concentration of fluorine
Figure 8. Repartition of P between substitutional sites and vacancy complexes, density of mono-vacancies and free electron concentration as a function of the total number of vacancies present in the sample (Ptotal = 2x1020 cm-3, no fluorine). The intersection between the calculated free electron concentration, n and the experimentally observed nmax of ~5x1019 cm-3 for Vtotal = 5x1019 cm-3 indicates that this is a reasonable estimate of the residual vacancy concentration in the sample after implantation and RTA at 600°C. Figure 8 shows the result of this model in the absence of fluorine for a temperature of 600°C and a chemical concentration of phosphorus corresponding to its solid solubility in germanium (2x1020 cm-3), treating the total number of vacancies as an unknown variable. For a small number of vacancies, most phosphorus atoms are substitutional, and the activation level is close to 100%. However, as the number of vacancies increase, so does the number of PV associates, resulting in a drop in the free carrier concentration. When the free electron concentration becomes too low, the formation of PV centers becomes unfavorable, and mono-vacancies dominate the vacancy population. Experimentally, the free carrier concentration is capped at 5x1019 cm-3, which for a phosphorus concentration of 2x1020 cm-3 corresponds to a total concentration of vacancies of 5x1019 cm-3 (intersection of the experimental and modeled free carrier concentrations in Figure 8), which serves as an approximation of the number of vacancies present in the material. Next, we model how the fluorine dose influences the free carrier concentration, for example in Figure 9, the free electron concentration is plotted as a function of the fluorine dose, for total vacancy concentrations of 2.5x1019 cm-3, 5x1019 cm-3 and 7.5x1019 cm-3, respectively. Figure 9. Free electron concentration versus fluorine concentration, for different vacancy concentrations, at 600°C. The influence of fluorine on the activation of phosphorus scales linearly with the dose until the concentration of fluorine