Minimal ohmic contact resistance limits to n -type semiconductors

An exact general formula for the lower contact resistance limit is derived, giving the lowest possible ohmic contact resistance for nondegenerate and degenerate metal-semiconductor contacts. Calculations for nondegenerate semiconductors include the nonparabolic nature of the conduction-band electrons and full Fermi–Dirac statistics. A discussion of standard emission theories shows that they are not applicable in the ohmic contact limit because of ‘‘electron tail lowering’’ and the negligence of quantum-mechanical reflections due to occupied states on the opposite side of their derivation. Together with a proof that an abrupt n-n+ doping step is governed by thermionic emission, the ohmic contact resistance of a general ohmic contact is determined and it is shown that the n-n+ doping step is responsible for this limitation. Thus, the lowest possible contact resistance is determined by the bulk doping of the semiconductor for a large variety of different alloyed and nonalloyed contact structures and not by the surface doping concentration. The theory predicts a lowest possible contact resistance in the 1 × 10−8 Ω cm2 region for parabolic III-V semiconductors and of about 3 × 10−9 Ω cm2 for Si and Ge.