Electronic band-edge properties of rock

Abstract

The electronic band-edges of lead chalcogenides PbY and tin chalcogenides SnY (where Y = S, Se, and Te) are investigated by the means of a full-potential linearized augmented plane wave (FPLAPW) method and the local density approximation (LDA). All six chalcogenide binaries have similar electronic structures and density-of-states, but there are differences in the symmetry of the band-edge states at and near the Brillouin zone L-point. These differences give the characteristic composition, pressure, and temperature dependences of the energy gap in Pb1 xSnxY alloys. We find that: (1) SnY are zero-gap semiconductors Eg = 0 if the spin–orbit (SO) interaction is excluded. The reason for this is that the conduction band (CB) and the valence band (VB) cross along the Q LW line. (2) Including the SO interaction splits this crossing and creates a direct gap along the Q-line, thus away from the L symmetry point. Hence, the fundamental band gap Eg in SnY is induced by the SO interaction and the energy gap is rather small Eg 0.2–0.3 eV. At the L-point, the CB state has symmetric Lþ4 and the VB state is antisymmetric L 4 thereby the L-point pressure coefficient oEgðLÞ=op is a positive quantity. (3) PbY have a direct band gap at the L-point both when SO coupling is excluded and included. In contrast to SnY, the SO interaction decreases the gap energy in PbY. (4) Including the SO interaction, the LDA yields incorrect symmetries of the band-edge states at the L-point; the CB state has Lþ4 and the VB state has L 4 symmetry. However, a small increase of the cell volume corrects this LDA failure, producing an antisymmetric CB state and a symmetric VB state, and thereby also yields the characteristic negative pressure coefficient oEgðLÞ=op in agreement with experimental findings. (5) Although PbY and SnY have different band-edge physics at their respective equilibrium lattice constants, the change of the band-edges with respect to cell volume is qualitatively the same for all six chalcogenides. (6) Finally, in the discussion of the symmetry of the band edges, it is important to clearly state the chosen unit cell origin; a shift by (a/2,0,0) changes the labeling Lþ4 () L 4 of the irreducible representations.