We theoretically identify the chemical thermodynamic boundary conditions that will produce -type via halogen doping. Remarkably, we find that due to the low formation energies of the intrinsic defects, and in , the growth conditions that maximize the halogen donor incorporation do not yield -type conductivity, whereas the conditions that maximize the concentration of the intrinsic donor do yield -type conductivity. Under the latter conditions, however, the contribution of the halogen donors to the net donor concentration stays significantly below that of .
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Instead of using the simplification , as used in most textbook examples, the Fermi–Dirac distribution function is integrated numerically to obtain and . Accordingly, there is no assumption necessary that is separated from the band edges by .