The dependence of electron density (ns) on AlGaN barrier thickness (dAlGaN) was studied for AlGaN/GaN single heterostructures whose dAlGaN was controlled by low-power Cl-based reactive ion etching (RIE) instead of growth. The samples showed a constant increase not only in ns but also in AlGaN surface barrier height (eϕB) with dAlGaN, indicating the existence of low-density and distributed donor states on the AlGaN surface. Such a distribution of donor states differs from the commonly accepted model based on high-density and single-level surface donor states as the source of electrons in the two-dimensional electron gas (2DEG). The presence of a distribution of donor states is confirmed by first-principles calculations for a variety of surface structures for oxidized AlGaN surfaces. Donor states arise from areas of the surface that deviate from the electron-counting rule, leading to occupied surface states in the upper half of the band gap. The oxide formed on the surface after RIE results in a low-density distribution of surface donor states in which the highest occupied levels span the range from 1–2 eV below the AlGaN conduction-band minimum. The density of these states is comparable to the ns in the 2DEG and insufficient to pin the Fermi level, leading to a constant increase in eϕB with dAlGaN.

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