A comprehensive thermodynamic analysis of native point defect and dopant solubilities in gallium arsenide

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Abstract
A detailed analysis of the role of charged native point defects in controlling the solubility of electrically active dopants in gallium arsenide is presented. The key roles of (a) positively charged arsenic vacancies (VAs+) in determining the doping range over which the solubility curve is linear and (b) multiply negative charged gallium vacancies (VGam−) determining annealing and diffusion behavior in n+ material are demonstrated. An equilibrium thermodynamic model based on these concepts is shown to accurately describe the doping behavior of Te, Zn, Sn, Ge, Si, and C and the formation and annealing of the deep level denoted EL2 (assumed to be the arsenic antisite defect AsGa) in melt- and solution-grown crystals. The model provides a much more comprehensive and accurate description of dopant solubility than the widely cited Schottky barrier model of bulk nonequilibrium dopant incorporation. It is unambiguously shown that partial autocompensation of donor dopants by the donor–gallium vacancy acceptor complex occurs for both group IV and group VI donor dopants. The deduced concentrations of arsenic vacancies grown into the crystal during melt growth are shown to be in excellent agreement with values determined by titration and by density/lattice parameter measurements. The obtained data are used to plot the Ga–As solidus. Due to the presence of charged native point defect species (notably, VAs+), the free-carrier concentration at high temperatures is greater than the intrinsic concentration. The calculated concentration is shown to be in excellent agreement with published experimental data. The utility of an equilibrium thermodynamic model in seeking an understanding of doping behavior under conditions of high supersaturation, such as occur with organometallic vapor phase epitaxy and molecular beam epitaxy, is demonstrated. Finally, some suggestions are made as to the likely native point defect equilibria in indium phosphide.