Isotopic Effects in the Phonon and Electron Dispersion Relations of Crystals

Abstract

During the past ten years, the relaxation of international tensions between East and West has resulted in the so‐called “peace dividends”. Among these dividends, solid state physicists have profited from the increasing availability of stable isotopes of many elements at affordable prices. These isotopes originate sometimes in the United States and sometimes in Russia. They can either be purchased or obtained “on loan” on the basis of scientific collaboration. With these isotopes, single crystals with tailor‐made isotopic compositions have been grown. Using these crystals, information on a number of rather basic physical properties has been obtained. We discuss in this review the following properties of such semiconductor crystals: 1. dependence of the lattice parameters on isotopic masses; 2. effect of isotopic disorder on thermal conductivity; 3. anharmonic effects on the phonon frequencies and linewidths and their dependence on isotopic mass; 4. effects of isotopic disorder on phonon frequencies and linewidhts; 5. renormalization of the energy of electronic states through electron–phonon interaction; and 6. self‐diffusion of atoms in crystals. Because of space limitations this discussion will not be exhaustive. We hope, however, to give sufficient references to published work so that the interested reader can easily find the primary literature sources to this rapidly expanding field of solid state physics. (A few multilingual short reviews are listed under [1].)

Fundamentals and Applications of Isotope Effect in Modern Technology

“…7)), whereas in the case of germanium it is the highest point. 12) This shift of the maximum from the À-point (k¼0) leads to a much larger density of states in the vicinity of ! LTO in comparison with the normal one calculated by the formula:…”

Refractive index spectral dependence, Raman spectra, and transmission spectra of high-purity Si28, Si29, Si30, and Sinat single crystals

“…With no absorption, the refractive index equals to n (ω) = ε 1/2 (ω). The fundamental absorption edge energies depend on isotopic composition and for an isotopically pure crystal can be expressed as [26][27][28]:…”

Isotope effect on phonon spectra in single-walled carbon nanotubes

“…In the isotope doped systems, if the mass fluctuation is not very large, it may be a good first-order approximation to replace the mass of C-atom by the weighted average mass of the isotopes, 21 namely…”

“…To the best of knowledge of the present authors, there is no theoretical attempt in carbon nanotube systems, though the isotope effect on phonons in semiconductor superlattices has been investigated by Cardona group extensively. [18][19][20][21] The paper is organized as follows. After the Introduction, we shall first introduce several typical isotope doping configurations for study, and specify the atomic arrangements in each configuration.…”