Effect of isotopic disorder and mass on the electronic and vibronic properties of three-, two- and one-dimensional solids

Abstract

Most natural elements contain several isotopes. Single crystals grown from them are disordered systems in which the translational invariance is violated by the isotopic mass disorder. Its effects on the vibrational properties of solids of various dimensions are discussed and illustrated with examples involving germanium and diamond. Such effects are often the stronger the lower the dimensionality. Their vibrational frequencies vary rather accurately as the 'average' isotopic mass M. Hence, the average zero-point (i.e. low-temperature) vibrational amplitude varies as M-12/. This leads to changes in many physical properties with average isotopic mass, many of which have been calculated and measured. Among them the authors discuss: the lattice constant, the thermal conductivity, the phonon lifetimes and the electronic gap energies and Lorentzian widths. The possibility of doping superlattices and MQW with layers made of different isotopes is also discussed. Experiments involving isotopically enriched surfaces and thin films are suggested.