Diffusion via native defects, and the appropriate choice of independent thermodynamic variables in both quasi-equilibriu
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It is clear from this that PGa is defined once T and PAs are chosen. However, the phase rule does not demand that one control T. One might insist on picking PAs and PGa as the two independent variables, and indeed this choice does define the equilibrium state of the crystal. Of course, such a choice makes T a dependent variable (via eq 1). The sufficient condition for an experiment to approach equilibrium in a useful time is satisfied only by using an experimental design which makes sure that the equilibrium value of T can be attained in an appropriate time. For example, if one placed the system in a furnace which was preheated to the calculated temperature, and if solid-vapor equilibrium were attained in a time short compared to the time of the entire anneal, then one might be able to draw conclusions about marker diffusion, impurity solubility, etc., using a simple quasi-equilibrium model. However, if one depended upon the exothermic reaction between Ga and As added to the vapor to heat a GaAs substrate to the calculated equilibrium temperature, then the crystal might not reach equilibrium for a long time, and one must use more complicated nonequilibrium models to interpret the observed materials properties. DISCUSSION
If it is possible for the GaAs crystal to approach equilibrium with the vapor in a usefully short time, then it makes sense to think about changing the equilibrium crystal stoichiometry, i.e., in the native defect concentrations, using a phase diagram. Fig. I shows the T-X slice of the GaAs phase diagram. Although it is often useful to think of GaAs as a line compound, Fig. 1 explicitly shows an exaggerated solidus line to illustrate that the equilibrium crystal stoichiometry depends explicitly upon the annealing ambient. For example, at any chosen temperature the most Ga-rich equilibrium crystal will be obtained when annealing at three phase equilibrium between vapor, GaAs, and liquid Ga (saturated with As), and the most As-rich equilibrium crystal will be obtained when annealing at three phase equilibrium between vapor, GaAs, and condensed As (saturated with Ga). However, if the average composition of the system lies between the solidus lines, then GaAs is the only condensed phase present and generally the equilibrium PGa and PAs can vary by many orders of magnitude. As discussed elsewhere,' the variations in stoichiometry can be directly related to the change in concentration of the six native point defects: the Ga vacancy, VGa, and interstitial, IGa, the As vacancy, VAs, and interstitial, IAs, and the Ga and As antisites, GaAs and ASGa, respectively. Since material properties such as diffusion depend upon the concentration of one or more native defects, it is worth relating some properties to native defect equilibrium before discussing deviations away from equilibrium. Although any discussion of 'diffusion at equilibrium' is inherently an oxymoron, one can carefully discuss the diffusion of marker atoms in a crystal containing native point defect concentrations at their equilibrium values. Th
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