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The ionization energies of different charge states must be known to estimate a charge of a defect. It is obvious that ionization energies of vacancies and vacancy-assisted complexities depend on the temperature, but there are no reliable data of that energies [15, 31–37]. In [36] it was shown that at equilibrium conditions, half occupancy of the doubly negatively charged state of the vacancy-group-V-impurity atom pairs occurs when the Fermi level is situated at the middle of the forbidden gap. In spite of large phosphorus concentrations, n in the case of our interest is comparatively small, Fermi level is near the middle of the forbidden gap, and we

n3 <sup>0</sup> �<sup>1</sup> ð Þ PV �<sup>1</sup> <sup>¼</sup> <sup>P</sup><sup>þ</sup> <sup>þ</sup> <sup>V</sup><sup>0</sup> <sup>þ</sup> 2e� <sup>0</sup> �<sup>2</sup> ð Þ PV �<sup>2</sup> <sup>¼</sup> <sup>P</sup><sup>þ</sup> <sup>þ</sup> <sup>V</sup><sup>0</sup> <sup>þ</sup> <sup>3</sup>e�

As the electron density increases, the charge state of the pair can change. In the depletion region of the first p-n junction together with sharp increase of the Fermi level, the amount and

In spite of numerous P in Ge diffusivity investigations, there are some issues that remain unclarified. The first one is the discrepancies between intrinsic diffusivities, calculated from Fickean type of diffusion profile at low phosphorus concentrations and those calculated using Boltzmann-Matano method from diffusion profiles at high P concentration. If we agree with vacancy assistant diffusion model, it means that P introduction into Ge increases the total

The formation of a p-n junction for germanium cascade of multiple solar cells due to the diffusion of phosphorus from the buffer layer In0.56Ga0.44P of In0.01Ga0.99As/In0.56Ga0.44P/Ge heterostructure leads to co-diffusion of P and Ga. The process was held at 635�C for 2.6 min.

charge of the pairs can be changed drastically, leading to a sharp increase in DP.

CP = n CP = const k j k j

n0 �2 0 ð Þ PV <sup>0</sup> <sup>þ</sup> <sup>e</sup>� <sup>¼</sup> <sup>P</sup><sup>þ</sup> <sup>þ</sup> <sup>V</sup>�<sup>2</sup> �1 0 ð Þ PV <sup>0</sup> <sup>¼</sup> <sup>P</sup><sup>þ</sup> <sup>þ</sup> <sup>V</sup>�<sup>1</sup>

n1 �1 0 ð Þ PV <sup>0</sup> <sup>¼</sup> <sup>P</sup><sup>þ</sup> <sup>þ</sup> <sup>V</sup> 0 0 ð Þ PV <sup>0</sup> <sup>¼</sup> <sup>P</sup><sup>þ</sup> <sup>þ</sup> <sup>V</sup><sup>0</sup> <sup>þ</sup> <sup>e</sup>�

�<sup>3</sup> �<sup>1</sup> ð Þ PV �<sup>1</sup> <sup>þ</sup> <sup>e</sup>� <sup>¼</sup> <sup>P</sup><sup>þ</sup> <sup>þ</sup> <sup>V</sup>�<sup>3</sup> �<sup>2</sup> �<sup>1</sup> ð Þ PV �<sup>1</sup> <sup>¼</sup> <sup>P</sup><sup>þ</sup> <sup>þ</sup> <sup>V</sup>�<sup>2</sup>

�<sup>2</sup> �<sup>1</sup> ð Þ PV �<sup>1</sup> <sup>¼</sup> <sup>P</sup><sup>þ</sup> <sup>þ</sup> <sup>V</sup>�<sup>2</sup> �<sup>1</sup> �<sup>1</sup> ð Þ PV �<sup>1</sup> <sup>¼</sup> <sup>P</sup><sup>þ</sup> <sup>þ</sup> <sup>V</sup>�<sup>1</sup> <sup>þ</sup> <sup>e</sup>� �<sup>3</sup> �<sup>2</sup> ð Þ PV �<sup>2</sup> <sup>¼</sup> <sup>P</sup><sup>þ</sup> <sup>þ</sup> <sup>V</sup>�<sup>3</sup> �<sup>2</sup> �<sup>2</sup> ð Þ PV �<sup>2</sup> <sup>¼</sup> <sup>P</sup><sup>þ</sup> <sup>þ</sup> <sup>V</sup>�<sup>2</sup> <sup>þ</sup> <sup>e</sup>�

�<sup>1</sup> �<sup>1</sup> ð Þ PV �<sup>1</sup> <sup>¼</sup> <sup>P</sup><sup>þ</sup> <sup>þ</sup> <sup>V</sup>�<sup>1</sup> <sup>þ</sup> <sup>e</sup>� �<sup>1</sup> �<sup>2</sup> ð Þ PV �<sup>2</sup> <sup>¼</sup> <sup>P</sup><sup>þ</sup> <sup>þ</sup> <sup>V</sup>�<sup>1</sup> <sup>þ</sup> <sup>2</sup>e�

�<sup>3</sup> �<sup>2</sup> ð Þ PV �<sup>2</sup> <sup>¼</sup> <sup>P</sup><sup>þ</sup> <sup>þ</sup> <sup>V</sup>�<sup>3</sup>

<sup>þ</sup> <sup>e</sup>� <sup>0</sup> �<sup>1</sup> ð Þ PV �<sup>1</sup> <sup>¼</sup> <sup>P</sup><sup>þ</sup> <sup>þ</sup> <sup>V</sup><sup>0</sup> <sup>þ</sup> <sup>2</sup>e�

may suggest that the (27) is an achievement.

n2 0 0 ð Þ PV <sup>0</sup> <sup>¼</sup> <sup>P</sup><sup>þ</sup> <sup>þ</sup> <sup>V</sup>0K

42 Advanced Material and Device Applications with Germanium

�<sup>2</sup> �<sup>2</sup> ð Þ PV �<sup>2</sup> <sup>¼</sup> <sup>P</sup><sup>þ</sup> <sup>þ</sup> <sup>V</sup>�<sup>2</sup> <sup>þ</sup> <sup>e</sup>�

�<sup>1</sup> �<sup>2</sup> ð Þ PV �<sup>2</sup> <sup>¼</sup> <sup>P</sup><sup>þ</sup> <sup>þ</sup> <sup>V</sup>�<sup>1</sup> <sup>þ</sup> 2e�

Table 1. Equations and parameters for different dependencies of <sup>D</sup>ð Þ PV <sup>j</sup> on <sup>n</sup>.

5. Conclusions

vacancy concentration.

Kobeleva Svetlana Petrovna\*, Iliya Anfimov and Sergey Yurchuk

\*Address all correspondence to: kob@misis.ru

National University of Science and Technology "MISiS", Moscow, RF, Russia
