The polar interface between LaAlO$_{3}$ and SrTiO$_{3}$ has shown promise as a field effect transistor, with reduced (nanoscale) feature sizes and potentially added functionality over conventional semiconductor systems. However, the mobility of the interfacial two-dimensional electron gas (2DEG) is lower than desirable. Therefore to progress, the highly debated origin of the 2DEG must be understood. Here we present a case for surface redox reactions as the origin of the 2DEG, in particular surface O vacancies, using a model supported by first principles calculations that describes the redox formation. In agreement with recent spectroscopic and transport measurements, we predict a stabilization of such redox processes (and hence Ti 3$d$ occupation) with film thickness beyond a critical value, which can be smaller than the critical thickness for 2D electronic conduction, since the surface defects generate trapping potentials that will affect the interface electron mobility. Several other recent experimental results, such as lack of core level broadening and shifts, find natural explanation. Pristine systems will likely require changed growth conditions or modified materials with a higher vacancy free energy.
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