A thermodynamic analysis of native point defect and dopant solubilities in zinc-blende III–V semiconductors

Abstract

A thermodynamic model is used to analyze available experimental data relevant to point defects in the binary zinc-blende III–V compounds (Ga,In)-(P,As,Sb). The important point defects and their complexes in each of the materials are identified and included in the model. Essentially all of the available experimental data on dopant solubility, crystal density, and lattice parameter of melt and solution grown crystals and epilayers are reproduced by the model. It extends an earlier study [Hurle, J. Appl. Phys. 85, 6957 (1999)] devoted solely to GaAs. Values for the enthalpy and entropy of formation of both native and dopant related point defects are obtained by fitting to experimental data. In undoped material, vacancies, and interstitials on the Group V sublattice dominate in the vicinity of the melting point (MP) in both the phosphides and arsenides, whereas, in the antimonides, vacancies on both sublattices dominate. The calculated concentrations of the native point defects are used to construct the solidus curves of all the compounds. The charged native point defect concentrations at the MP in four of the six materials are significantly higher than their intrinsic carrier concentrations. Thus the usually assumed high temperature “intrinsic” electroneutrality condition for undoped material (n=p) is not valid for these materials. In GaSb, the GaSb antisite defect appears to be grown-in from the melt. This contrasts with the AsGa defect in GaAs for which the concentration grown-in at the MP is negligibly small. Compensation of donor-doped material by donor-Group III vacancy complexes is shown to exist in all the compounds except InP where Group VI doped crystals are uncompensated and in InSb where there is a lack of experimental data. The annealing effects in n+ GaAs, including lattice superdilation, which were shown in the earlier paper to be due to Group III vacancy undersaturation during cooling, are found to be present also in GaSb and InAs. Results for native point defects are compared with reported “first principles” calculations for GaAs. It is seen that, while there is some accord with experimental findings for low temperature molecular beam epitaxial (MBE) growth, they fail totally to predict the behavior under high temperature growth conditions. The analysis of data on liquid phase epitaxy (LPE) growth of GaAs from Bi solution in the earlier paper has been re-calculated in the light of experimental data that showed that the model used in that paper to represent the Ga–As–Bi phase equilibria was inadequate. An improved model reveals that Ga vacancies exert a greater effect in controlling the extent of the linear range of donor dopant solubility than previously predicted. It has also led to a re-evaluation of the equilibrium EL2 and Ga vacancy concentrations in GaAs during MBE growth under As-rich conditions at low temperatures (∼500 K). The amended model predicts that the very high concentrations of EL2 and of Ga vacancies observed experimentally are near equilibrium values. The predicted increase in the equilibrium concentrations of these defects at low temperatures results from coulombic attraction between the two defects. At temperatures somewhat lower than 500 K the rate of increase becomes catastrophic.