5. Conclusions

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 vacancy concentration.

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. Solubility of Ga in the InGaP/Ge interface is higher than of P that leads to formation of two p-n junctions. Co-doping by gallium strongly affects the diffusion of phosphorus in germanium. We propose that it occurs primarily due to the electric field of the forming p-n junctions. P-type region is formed in the thin Ge surface layer (30 nm of order) with the depletion region thickness of 8–10 nm. The electric field of this p-n junction is directed to the Ge surface and accelerates both negatively charged Ga in interstitial positions and vacancy-phosphorus pairs. That leads to comparatively high gallium diffusivity DGa = 1.4 <sup>10</sup><sup>15</sup> cm<sup>2</sup> /s.

We can point out that in the case of Ga and P co-diffusion, calculations of diffusivity by Sauer-Freise and coordinate dependence diffusion methods give values an order of magnitude higher than the values, obtained for quadratic and cubic diffusion model for phosphorus diffusion. An electric field of a depletion region of p-n junctions leads to the appearance of drift components of phosphorus diffusion. At low electron concentrations in p-region near Ge surface in which there is no an electric field, phosphorus diffusivity increases with n from intrinsic diffusivity values, produced from Fickean-type profiles at low P concentration, to that one calculated by Boltzmann-Matano method for high P concentrations, while P concentration sharply decreases. We may suppose the vacancy concentration increasing as the concentration of Ga and P that occupied the vacancies decreased.

It can be assumed that the electric field causes not only the appearance of a drift component in diffusion but also increases the diffusivity of P-V pairs. The sharp diffusivity growth and drop are consistent with the electric field direction. In the first p-n junction, it is directed to the surface and accelerates negatively charged particles including Ga and (PV). In the second one, it is directed into the sample that leads to decrease of the D(PV).

For a correct description of the Ga and P co-diffusion, it is necessary to take into account both changes in the concentration of charged centers due to a change in the Fermi level position and the formation and decay of diffusing pairs. For this, in the continuity equation, it is necessary to take into account not only the drift component but also the generation-recombination terms corresponding to the formation and decomposition of the diffusing pairs.
