Exchange-correlation effects in silicon (111) inversion layers: Strain-enhanced valley-occupancy phase transition

For multivalley systems, scaling relations, which are exact in the random-phase approximation (RPA), are derived which relate the exchange-correlation energy per particle of a $v$-valley system to that of a degenerate electron gas. These potentials are used in a local density-functional calculation of the ground-state energy of a Si(111) inversion layer. The exchange-correlation effects together with a small spontaneous lattice distortion greatly reduce the magnitude of the random interfacial strain needed to account for the observed valley degeneracies seen on many Si surfaces.