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We used the LDA formalism of L. Hedin and B. I. Lundqvist [J. Phys. C 4, 2064 (1971)]. See Eqs. (8)-(10) in F. Stern and S. Das Sarma, Phys. Rev. B 30, 840 (1984).
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It is at first glance surprising that the ideal BLES calculation always predicts a smaller charger transfer than the LDA, considering that tunneling is expected to reduce the charge transfer [H. Totsuji, Appl. Phys. Lett. 66, 3343 (1995)]. This can be explained qualitatively by noting that the capacitive energy cost of transferring charge depends directly on the distance transferred. Taking sample B as an example, we note that the inside edges of the quantum wells are only 30 Å apart, the centers are 170 Å apart, and the outside edges are 210 Å apart. In the ideal calculation, all of the electrons must transfer across 170 Å. In the LDA, those that transfer across 30 Å pay a capacitive energy cost of less than one fifth of what the ideal case electrons pay, while those that transfer across 210 Å, pay about 1.24 times as much as the ideal case electrons. Because of this difference in energy cost, the broader layers should show a greater charge transfer than the ideal ones. Therefore, in going from the ideal to the real case, charge transfer is increased by the reduced energy cost more than it is decreased by the possibility of tunneling.
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On the (100) substrate, Si is incorporated as a donor, while on the (311)A substrate it is incorporated as an acceptor. See M. B. Santos, J. Jo, Y. W. Suen, L. W. Engel and M. Shayegan, Phys. Rev. B 46, 13 693 (1992), and references therein.
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