Quantum confinement, surface roughness, and the conduction band structure of ultrathin silicon membranes

We report direct measurements of changes in the conduction-band structure of ultrathin silicon nanomembranes with quantum confinement. Confinement lifts the 6-fold-degeneracy of the bulk-silicon conduction-band minimum (CBM), Delta, and two inequivalent sub-band ladders, Delta(2) and Delta(4), form. We show that even very small surface roughness smears the nominally steplike features in the density of states (DOS) due to these sub-bands. We obtain the energy splitting between Delta(2) and Delta(4) and their shift with respect to the bulk value directly from the 2p(3/2)-->Delta transition in X-ray absorption. The measured dependence of the sub-band splitting and the shift of their weighted average on degree of confinement is in excellent agreement with theory, for both Si(001) and Si(110).