Thermodynamic calculations of self- and hetero-diffusion parameters in germanium

In the present work, the diffusion coefficients of n- and p-type dopants (P, As, Sb, Al) and self-diffusion in crystalline germanium are calculated from the bulk elastic properties of the host material based on the cBΩ thermodynamic model. The calculated diffusion coefficients as a function of temperature and the activation enthalpies prove to be in full agreement with the reported experimental results. Additional point defect parameters such as activation entropy, activation volume and activation Gibbs free energy are also calculated for each diffusing element. The pressure dependence of self-diffusion coefficients in germanium is also verified at high temperatures (876 K-1086 K), in agreement with reported results ranging from ambient pressure up to 600 MPa and is further calculated at pressures up to 3 GPa, where the phase transition to Ge II occurs.