Experimental Determination of Diffusion and Formation Energies of Thermal Vacancies in Germanium

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Intrinsic germanium semiconductor specimens with various dislocation densities were quenched from high temperatures to introduce vacancies, after purification by the surface oxidation technique. The contamination due to copper atoms diffused into these specimens was below 1×10¹³ atoms/c.c.. Annealing curves of exponential decay type were observed for specimens with dislocation densities (n_D∼5×10³∼10⁵). The activation energy for diffusion and diffusion are found to be: 1.2∼1.3 eV and D_V(T)=2×exp(−1.2eV⁄kT)cm²/sec..
After annealing of quenched-in vacancies, copper atoms were introduced into the specimens by diffusion procedures. By the analysis of precipitating manner of supersaturated copper atoms thus introduced, the formation energy of a vacancy is found to be 1.9 eV. Considering the number of quenched-in vacancies obtained by the quenching experiments, the concentration of quenched-in vacancies is concluded to be: N_V(T)=1.85×10²³exp(−1.9eV⁄kT)/c.c..