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note
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It might seem puzzling that the positive microscopic dipole of Fig. 2 and the negative macroscopic dipole of Figs. 1 and 2) yield identical, rather than opposing barrier height trends. However, it is found for both Schottky barriers and heterojunctions that identical (opposing) macroscopic-microscopic dipole polarities produce opposing (identical) trends in terms of barrier height. Perhaps the easiest way to understand this subtle, counterintuitive trend is to employ an interfacial layer of atomic dimensions to account for the finite separation distance of the microscopic dipole (e.g., see Ref. [17]). Next, recognize that the separation of charge across this interfacial layer due to the presence of a microscopic dipole essentially takes charge away from the metal side and places it onto the semiconductor side of the interfacial layer. Since this charge is now in closer physical proximity to the semiconductor, its effect is enhanced, in terms of barrier height modification, in the same sense as original the macroscopic dipole.
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18
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20
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22
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C is confusing, and is a consequence of the convergence of several energy band diagram sign conventions which are implicitly employed in Eqs. (7) and (11); electron energy is positive going upward, hole energy is positive going downward, electrostatic potential is positive going downward, and band gap is a positive quantity.
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