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Band offsets at lattice-mismatched heterojunctions can be tuned owing to their dependence on macroscopic strain, and hence on the substrate composition. The system studied here, GaAs/Si(001), is lattice mismatched and heterovalent, offering thus an additional flexibility, due to the intrinsic nonbulk character of the band offset at heterovalent junctions. Starting with a study of macroscopic and microscopic elasticity, we evaluate the band offset for several fully relaxed inequivalent interfaces. Both macroscopic strain and microscopic morphology strongly affect the offset between the topmost Si and GaAs valence bands, which, consequently, is tunable, in principle, by as much as 1.1 eV.

We perform a first-principles calculation of the static dielectric constant of Si in the framework of density-functional theory. The only essential approximation used in this work is the local-density approximation (LDA): norm-conserving pseudopotentials and large plane-wave basis sets are used, numerical roundoff and convergence errors are kept below 1%. The present calculation gives for the first time the ``exact'' value of the macroscopic dielectric constant at the LDA level. The theoretical value of ${\ensuremath{\epsilon}}_{\ensuremath{\infty}}$ is 12% higher than experiment.

The macroscopic polarizability of silicon is calculated from first principles as a function of the lattice distortion induced by a zone-center optical phonon. The electronic response to the electric field is dealt with by dielectric matrices, and the lattice distortion is treated by frozen-phonon techniques. Our results compare quite well with the most recent measurements of the one-phonon Raman cross section.