An approximation to density functional theory for an accurate calculation of band-gaps of semiconductors

摘要

The local-density approximation (LDA), together with the half-occupation(transition state) is notoriously successful in the calculation of atomicionization potentials. When it comes to extended systems, such as asemiconductor infinite system, it has been very difficult to find a way tohalf-ionize because the hole tends to be infinitely extended (a Bloch wave).The answer to this problem lies in the LDA formalism itself. One proves thatthe half-occupation is equivalent to introducing the hole self-energy(electrostatic and exchange-correlation) into the Schroedinger equation. Theargument then becomes simple: the eigenvalue minus the self-energy has to beminimized because the atom has a minimal energy. Then one simply proves thatthe hole is localized, not infinitely extended, because it must have maximalself-energy. Then one also arrives at an equation similar to the SIC equation,but corrected for the removal of just 1/2 electron. Applied to the calculationof band gaps and effective masses, we use the self-energy calculated in atomsand attain a precision similar to that of GW, but with the great advantage thatit requires no more computational effort than standard LDA.