Electronic structure of semiconductor quantum films

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Abstract
The electronic structure of thin (≤30 Å) free-standing ideal films of Si(001), Si(110), and GaAs(110) is calculated using a plane-wave pseudopotential description. Unlike the expectation based on the simple effective-mass model, we find the following. (i) The band gaps of (001) quantum films exhibit even-odd oscillation as a function of the number N of monolayers. (ii) In addition to sine-type envelope functions which vanish at the film boundaries, some states have cosine envelope functions with extrema at boundaries. (iii) Even-layer Si(001) films exhibit at the valence-band maximum a state whose energy does not vary with the film thickness. Such zero confinement states have constant envelope throughout the film. (iv) Optical transitions in films exhibit boundary-imposed selection rules. Furthermore, oscillator strengths for pseudodirect transitions in the vicinity of forbidden direct transitions can be enhanced by several orders of magnitude. These findings, obtained in direct supercell calculations, can be explained in terms of a truncated crystal (TC) analysis. In this approach the film’s wave functions are expanded in terms of pairs of bulk wave functions exhibiting a destructive interference at the boundaries. This maps the eigenvalue spectra of a film onto the bulk band structure evaluated at special k points which satisfy the boundary conditions. We find that the TC representation reproduces accurately the above-mentioned results of direct diagonalization of the film’s Hamiltonian. This provides a simple alternative to the effective-mass model and relates the properties of quantum structures to those of the bulk material.